diff --git a/include/fe/fe_lagrange_shape_1D.h b/include/fe/fe_lagrange_shape_1D.h
index 73da93158a4..318c5e59231 100644
--- a/include/fe/fe_lagrange_shape_1D.h
+++ b/include/fe/fe_lagrange_shape_1D.h
@@ -94,13 +94,36 @@ Real fe_lagrange_1D_cubic_shape(const unsigned int i,
 
 
 
+inline
+Real fe_lagrange_1D_any_shape(const Order order,
+                              const unsigned int i,
+                              const Real xi)
+{
+  libmesh_assert_greater_equal (order, 0);
+  libmesh_assert_less (i, order + 1);
+
+  // So the interval endpoints are at i = 0 and i = 1
+  const unsigned ii = i == 0 ? 0 : i == 1 ? int(order) : i - 1;
+
+  auto root = [&](const unsigned int k) { return 1. * k / order; };
+  const unsigned int nzeros = order + 1;
+  Real x = (xi + 1.) / 2.;
+  Real val = 1.;
+
+  for (const auto z : make_range(nzeros))
+    if (z != ii)
+      val *= (x - root(z)) / (root(ii) - root(z));
+
+  return val;
+}
+
+
+
 inline
 Real fe_lagrange_1D_shape(const Order order,
                           const unsigned int i,
                           const Real xi)
 {
-  libmesh_assert_less_equal(order, THIRD);
-
   switch (order)
     {
       // Lagrange linears
@@ -112,9 +135,12 @@ Real fe_lagrange_1D_shape(const Order order,
       return fe_lagrange_1D_quadratic_shape(i, xi);
 
       // Lagrange cubics
-      // case THIRD
-    default:
+    case THIRD:
       return fe_lagrange_1D_cubic_shape(i, xi);
+
+      // Lagrange arbitrary shape functions
+    default:
+      return fe_lagrange_1D_any_shape(order, i, xi);
     }
 }
 
@@ -196,14 +222,51 @@ Real fe_lagrange_1D_cubic_shape_deriv(const unsigned int i,
 
 
 
+inline
+Real fe_lagrange_1D_any_shape_deriv(const Order order,
+                                    const unsigned int i,
+                                    const unsigned int libmesh_dbg_var(j),
+                                    const Real xi)
+{
+  // only d()/dxi in 1D!
+  libmesh_assert_equal_to (j, 0);
+
+  libmesh_assert_greater_equal (order, 0);
+  libmesh_assert_less (i, order + 1);
+
+  // So the interval endpoints are at i = 0 and i = 1
+  const unsigned ii = i == 0 ? 0 : i == 1 ? int(order) : i - 1;
+
+  auto root = [&](const unsigned int k) { return 1. * k / order; };
+  const unsigned int nzeros = order + 1;
+  Real x = (xi + 1.) / 2.;
+  Real val = 0.;
+
+  for (const auto z : make_range(nzeros))
+    if (z != ii)
+    {
+      Real prod = .5;
+      for (const auto zz : make_range(nzeros))
+        if (zz != z && zz != ii)
+          prod *= (x - root(zz));
+      val += prod;
+    }
+
+  for (const auto z : make_range(nzeros))
+    if (z != ii)
+      val /= (root(ii) - root(z));
+
+  return val;
+}
+
+
+
 inline
 Real fe_lagrange_1D_shape_deriv(const Order order,
                                 const unsigned int i,
                                 const unsigned int j,
                                 const Real xi)
 {
-  libmesh_assert_less_equal(order, THIRD);
-
   switch (order)
     {
     case FIRST:
@@ -212,9 +275,11 @@ Real fe_lagrange_1D_shape_deriv(const Order order,
     case SECOND:
       return fe_lagrange_1D_quadratic_shape_deriv(i, j, xi);
 
-    // case THIRD
-    default:
+    case THIRD:
       return fe_lagrange_1D_cubic_shape_deriv(i, j, xi);
+
+    default:
+      return fe_lagrange_1D_any_shape_deriv(order, i, j, xi);
     }
 }
 
@@ -229,9 +294,9 @@ Real fe_lagrange_1D_quadratic_shape_second_deriv(const unsigned int i,
                                                  const unsigned int libmesh_dbg_var(j),
                                                  const Real)
 {
-  // Don't need to switch on j.  1D shape functions
-  // depend on xi only!
+  // Don't need to switch on j. 1D shape functions depend on xi only!
   libmesh_assert_equal_to (j, 0);
+
   libmesh_assert_less(i, 3);
 
   switch (i)
@@ -254,9 +319,9 @@ Real fe_lagrange_1D_cubic_shape_second_deriv(const unsigned int i,
                                              const unsigned int libmesh_dbg_var(j),
                                              const Real xi)
 {
-  // Don't need to switch on j.  1D shape functions
-  // depend on xi only!
+  // Don't need to switch on j. 1D shape functions depend on xi only!
   libmesh_assert_equal_to (j, 0);
+
   libmesh_assert_less(i, 4);
 
   switch (i)
@@ -278,14 +343,53 @@ Real fe_lagrange_1D_cubic_shape_second_deriv(const unsigned int i,
 
 
 
+inline
+Real fe_lagrange_1D_any_shape_second_deriv(const Order order,
+                                           const unsigned int i,
+                                           const unsigned int libmesh_dbg_var(j),
+                                           const Real xi)
+{
+  // Don't need to switch on j. 1D shape functions depend on xi only!
+  libmesh_assert_equal_to (j, 0);
+
+  libmesh_assert_greater_equal (order, 0);
+  libmesh_assert_less (i, order + 1);
+
+  // So the interval endpoints are at i = 0 and i = 1
+  const unsigned ii = i == 0 ? 0 : i == 1 ? int(order) : i - 1;
+
+  auto root = [&](const unsigned int k) { return 1. * k / order; };
+  const unsigned int nzeros = order + 1;
+  Real x = (xi + 1.) / 2.;
+  Real val = 0.;
+
+  for (const auto z : make_range(nzeros))
+    if (z != ii)
+      for (const auto zz : make_range(nzeros))
+        if (zz != z && zz != ii)
+        {
+          Real prod = .25;
+          for (const auto zzz : make_range(nzeros))
+            if (zzz != zz && zzz != z && zzz != ii)
+              prod *= (x - root(zzz));
+          val += prod;
+        }
+
+  for (const auto z : make_range(nzeros))
+    if (z != ii)
+      val /= (root(ii) - root(z));
+
+  return val;
+}
+
+
+
 inline
 Real fe_lagrange_1D_shape_second_deriv(const Order order,
                                        const unsigned int i,
                                        const unsigned int j,
                                        const Real xi)
 {
-  libmesh_assert_less_equal(order, THIRD);
-
   switch (order)
     {
     // All second derivatives of linears are zero....
@@ -295,9 +399,11 @@ Real fe_lagrange_1D_shape_second_deriv(const Order order,
     case SECOND:
       return fe_lagrange_1D_quadratic_shape_second_deriv(i, j, xi);
 
-    // case THIRD
-    default:
+    case THIRD:
       return fe_lagrange_1D_cubic_shape_second_deriv(i, j, xi);
+
+    default:
+      return fe_lagrange_1D_any_shape_second_deriv(order, i, j, xi);
     } // end switch (order)
 }
 
diff --git a/src/fe/fe_interface.C b/src/fe/fe_interface.C
index 4b9ef91e117..c49aa6d5656 100644
--- a/src/fe/fe_interface.C
+++ b/src/fe/fe_interface.C
@@ -2149,9 +2149,10 @@ unsigned int FEInterface::max_order(const FEType & fe_t,
       switch (el_t)
         {
         case EDGE2:
-        case EDGE3:
         case EDGE4:
           return 3;
+        case EDGE3:
+          return unlimited;
         case TRI3:
         case TRISHELL3:
         case C0POLYGON:
diff --git a/src/fe/fe_lagrange.C b/src/fe/fe_lagrange.C
index 88cf0fb6793..103d910eaa3 100644
--- a/src/fe/fe_lagrange.C
+++ b/src/fe/fe_lagrange.C
@@ -53,7 +53,22 @@ void lagrange_nodal_soln(const Elem * elem,
 
   nodal_soln.resize(n_nodes);
 
+  switch (type)
+    {
+    case EDGE3:
+      {
+        nodal_soln[0] = elem_soln[0];
+        nodal_soln[1] = elem_soln[1];
+        nodal_soln[2] = (totalorder % 2) ? 0 : elem_soln[totalorder / 2 + 1];
+        if (totalorder % 2)
+          for (unsigned i = 0; i < totalorder + 1; i++)
+            nodal_soln[2] += elem_soln[i] * FE<1,LAGRANGE>::shape(type, totalorder, i, 0);
 
+        return;
+      }
+    default:
+      ;
+    }
 
   switch (totalorder)
     {
@@ -62,18 +77,6 @@ void lagrange_nodal_soln(const Elem * elem,
       {
         switch (type)
           {
-          case EDGE3:
-            {
-              libmesh_assert_equal_to (elem_soln.size(), 2);
-              libmesh_assert_equal_to (nodal_soln.size(), 3);
-
-              nodal_soln[0] = elem_soln[0];
-              nodal_soln[1] = elem_soln[1];
-              nodal_soln[2] = .5*(elem_soln[0] + elem_soln[1]);
-
-              return;
-            }
-
           case EDGE4:
             {
               libmesh_assert_equal_to (elem_soln.size(), 2);
@@ -312,21 +315,6 @@ void lagrange_nodal_soln(const Elem * elem,
       {
         switch (type)
           {
-          case EDGE4:
-            {
-              libmesh_assert_equal_to (elem_soln.size(), 3);
-              libmesh_assert_equal_to (nodal_soln.size(), 4);
-
-              // Project quadratic solution onto cubic element nodes
-              nodal_soln[0] = elem_soln[0];
-              nodal_soln[1] = elem_soln[1];
-              nodal_soln[2] = (2.*elem_soln[0] - elem_soln[1] +
-                               8.*elem_soln[2])/9.;
-              nodal_soln[3] = (-elem_soln[0] + 2.*elem_soln[1] +
-                               8.*elem_soln[2])/9.;
-              return;
-            }
-
           case TRI7:
             {
               libmesh_assert_equal_to (elem_soln.size(), 6);
@@ -434,31 +422,25 @@ unsigned int lagrange_n_dofs(const ElemType t, const Elem * e, const Order o)
 {
   libmesh_assert(!e || e->type() == t);
 
-  switch (o)
+  switch (t)
     {
-      // lagrange can only be constant on a single node
-    case CONSTANT:
-      {
-        switch (t)
-          {
-          case NODEELEM:
-            return 1;
-
-          default:
-            libmesh_error_msg("ERROR: Bad ElemType = " << Utility::enum_to_string(t) << " for " << Utility::enum_to_string(o) << " order approximation!");
-          }
-      }
+    case NODEELEM:
+      return 1;
+    case EDGE3:
+      libmesh_error_msg_if(o == CONSTANT, "ERROR: Bad ElemType = " << Utility::enum_to_string(t) << " for " << Utility::enum_to_string(o) << " order approximation!");
+      return o + 1;
+    default:
+      ;
+    }
 
+  switch (o)
+    {
       // linear Lagrange shape functions
     case FIRST:
       {
         switch (t)
           {
-          case NODEELEM:
-            return 1;
-
           case EDGE2:
-          case EDGE3:
           case EDGE4:
             return 2;
 
@@ -522,12 +504,6 @@ unsigned int lagrange_n_dofs(const ElemType t, const Elem * e, const Order o)
       {
         switch (t)
           {
-          case NODEELEM:
-            return 1;
-
-          case EDGE3:
-            return 3;
-
           case TRI6:
           case TRI7:
             return 6;
@@ -577,9 +553,6 @@ unsigned int lagrange_n_dofs(const ElemType t, const Elem * e, const Order o)
       {
         switch (t)
           {
-          case NODEELEM:
-            return 1;
-
           case EDGE4:
             return 4;
 
@@ -617,31 +590,25 @@ unsigned int lagrange_n_dofs_at_node(const ElemType t,
                                      const Order o,
                                      const unsigned int n)
 {
-  switch (o)
+  switch (t)
     {
-      // lagrange can only be constant on a single node
-    case CONSTANT:
-      {
-        switch (t)
-          {
-          case NODEELEM:
-            return 1;
-
-          default:
-            libmesh_error_msg("ERROR: Bad ElemType = " << Utility::enum_to_string(t) << " for " << Utility::enum_to_string(o) << " order approximation!");
-          }
-      }
+    case NODEELEM:
+      return 1;
+    case EDGE3:
+      libmesh_error_msg_if(o == CONSTANT, "ERROR: Bad ElemType = " << Utility::enum_to_string(t) << " for " << Utility::enum_to_string(o) << " order approximation!");
+      return n < 2 ? 1 : o - 1;
+    default:
+      ;
+    }
 
+  switch (o)
+    {
       // linear Lagrange shape functions
     case FIRST:
       {
         switch (t)
           {
-          case NODEELEM:
-            return 1;
-
           case EDGE2:
-          case EDGE3:
           case EDGE4:
             {
               switch (n)
@@ -790,8 +757,6 @@ unsigned int lagrange_n_dofs_at_node(const ElemType t,
         switch (t)
           {
             // quadratic lagrange has one dof at each node
-          case NODEELEM:
-          case EDGE3:
           case TRI6:
           case QUAD8:
           case QUADSHELL8:
@@ -831,7 +796,6 @@ unsigned int lagrange_n_dofs_at_node(const ElemType t,
       {
         switch (t)
           {
-          case NODEELEM:
           case EDGE4:
           case PRISM20:
           case PRISM21:
diff --git a/tests/Makefile.am b/tests/Makefile.am
index 6f27e83ae14..e62c6d2da0d 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -44,6 +44,7 @@ unit_tests_sources = \
   fe/fe_test.h \
   fe/fe_xyz_test.C \
   fe/dual_shape_verification_test.C \
+  fe/fe_lagrange_shape_verification_test.C \
   geom/bbox_test.C \
   geom/edge_test.C \
   geom/elem_test.C \
diff --git a/tests/Makefile.in b/tests/Makefile.in
index 741fc6a7fc0..6b93c99983a 100644
--- a/tests/Makefile.in
+++ b/tests/Makefile.in
@@ -201,7 +201,8 @@ am__unit_tests_dbg_SOURCES_DIST = driver.C libmesh_cppunit.h \
 	fe/fe_lagrange_test.C fe/fe_monomial_test.C \
 	fe/fe_rational_map.C fe/fe_rational_test.C fe/fe_side_test.C \
 	fe/fe_szabab_test.C fe/fe_test.h fe/fe_xyz_test.C \
-	fe/dual_shape_verification_test.C geom/bbox_test.C \
+	fe/dual_shape_verification_test.C \
+	fe/fe_lagrange_shape_verification_test.C geom/bbox_test.C \
 	geom/edge_test.C geom/elem_test.C geom/elem_test.h \
 	geom/node_test.C geom/point_test.C geom/point_test.h \
 	geom/side_test.C geom/volume_test.C \
@@ -285,6 +286,7 @@ am__objects_2 = unit_tests_dbg-driver.$(OBJEXT) \
 	fe/unit_tests_dbg-fe_szabab_test.$(OBJEXT) \
 	fe/unit_tests_dbg-fe_xyz_test.$(OBJEXT) \
 	fe/unit_tests_dbg-dual_shape_verification_test.$(OBJEXT) \
+	fe/unit_tests_dbg-fe_lagrange_shape_verification_test.$(OBJEXT) \
 	geom/unit_tests_dbg-bbox_test.$(OBJEXT) \
 	geom/unit_tests_dbg-edge_test.$(OBJEXT) \
 	geom/unit_tests_dbg-elem_test.$(OBJEXT) \
@@ -404,7 +406,8 @@ am__unit_tests_devel_SOURCES_DIST = driver.C libmesh_cppunit.h \
 	fe/fe_lagrange_test.C fe/fe_monomial_test.C \
 	fe/fe_rational_map.C fe/fe_rational_test.C fe/fe_side_test.C \
 	fe/fe_szabab_test.C fe/fe_test.h fe/fe_xyz_test.C \
-	fe/dual_shape_verification_test.C geom/bbox_test.C \
+	fe/dual_shape_verification_test.C \
+	fe/fe_lagrange_shape_verification_test.C geom/bbox_test.C \
 	geom/edge_test.C geom/elem_test.C geom/elem_test.h \
 	geom/node_test.C geom/point_test.C geom/point_test.h \
 	geom/side_test.C geom/volume_test.C \
@@ -487,6 +490,7 @@ am__objects_4 = unit_tests_devel-driver.$(OBJEXT) \
 	fe/unit_tests_devel-fe_szabab_test.$(OBJEXT) \
 	fe/unit_tests_devel-fe_xyz_test.$(OBJEXT) \
 	fe/unit_tests_devel-dual_shape_verification_test.$(OBJEXT) \
+	fe/unit_tests_devel-fe_lagrange_shape_verification_test.$(OBJEXT) \
 	geom/unit_tests_devel-bbox_test.$(OBJEXT) \
 	geom/unit_tests_devel-edge_test.$(OBJEXT) \
 	geom/unit_tests_devel-elem_test.$(OBJEXT) \
@@ -602,7 +606,8 @@ am__unit_tests_oprof_SOURCES_DIST = driver.C libmesh_cppunit.h \
 	fe/fe_lagrange_test.C fe/fe_monomial_test.C \
 	fe/fe_rational_map.C fe/fe_rational_test.C fe/fe_side_test.C \
 	fe/fe_szabab_test.C fe/fe_test.h fe/fe_xyz_test.C \
-	fe/dual_shape_verification_test.C geom/bbox_test.C \
+	fe/dual_shape_verification_test.C \
+	fe/fe_lagrange_shape_verification_test.C geom/bbox_test.C \
 	geom/edge_test.C geom/elem_test.C geom/elem_test.h \
 	geom/node_test.C geom/point_test.C geom/point_test.h \
 	geom/side_test.C geom/volume_test.C \
@@ -685,6 +690,7 @@ am__objects_6 = unit_tests_oprof-driver.$(OBJEXT) \
 	fe/unit_tests_oprof-fe_szabab_test.$(OBJEXT) \
 	fe/unit_tests_oprof-fe_xyz_test.$(OBJEXT) \
 	fe/unit_tests_oprof-dual_shape_verification_test.$(OBJEXT) \
+	fe/unit_tests_oprof-fe_lagrange_shape_verification_test.$(OBJEXT) \
 	geom/unit_tests_oprof-bbox_test.$(OBJEXT) \
 	geom/unit_tests_oprof-edge_test.$(OBJEXT) \
 	geom/unit_tests_oprof-elem_test.$(OBJEXT) \
@@ -800,7 +806,8 @@ am__unit_tests_opt_SOURCES_DIST = driver.C libmesh_cppunit.h \
 	fe/fe_lagrange_test.C fe/fe_monomial_test.C \
 	fe/fe_rational_map.C fe/fe_rational_test.C fe/fe_side_test.C \
 	fe/fe_szabab_test.C fe/fe_test.h fe/fe_xyz_test.C \
-	fe/dual_shape_verification_test.C geom/bbox_test.C \
+	fe/dual_shape_verification_test.C \
+	fe/fe_lagrange_shape_verification_test.C geom/bbox_test.C \
 	geom/edge_test.C geom/elem_test.C geom/elem_test.h \
 	geom/node_test.C geom/point_test.C geom/point_test.h \
 	geom/side_test.C geom/volume_test.C \
@@ -883,6 +890,7 @@ am__objects_8 = unit_tests_opt-driver.$(OBJEXT) \
 	fe/unit_tests_opt-fe_szabab_test.$(OBJEXT) \
 	fe/unit_tests_opt-fe_xyz_test.$(OBJEXT) \
 	fe/unit_tests_opt-dual_shape_verification_test.$(OBJEXT) \
+	fe/unit_tests_opt-fe_lagrange_shape_verification_test.$(OBJEXT) \
 	geom/unit_tests_opt-bbox_test.$(OBJEXT) \
 	geom/unit_tests_opt-edge_test.$(OBJEXT) \
 	geom/unit_tests_opt-elem_test.$(OBJEXT) \
@@ -998,7 +1006,8 @@ am__unit_tests_prof_SOURCES_DIST = driver.C libmesh_cppunit.h \
 	fe/fe_lagrange_test.C fe/fe_monomial_test.C \
 	fe/fe_rational_map.C fe/fe_rational_test.C fe/fe_side_test.C \
 	fe/fe_szabab_test.C fe/fe_test.h fe/fe_xyz_test.C \
-	fe/dual_shape_verification_test.C geom/bbox_test.C \
+	fe/dual_shape_verification_test.C \
+	fe/fe_lagrange_shape_verification_test.C geom/bbox_test.C \
 	geom/edge_test.C geom/elem_test.C geom/elem_test.h \
 	geom/node_test.C geom/point_test.C geom/point_test.h \
 	geom/side_test.C geom/volume_test.C \
@@ -1081,6 +1090,7 @@ am__objects_10 = unit_tests_prof-driver.$(OBJEXT) \
 	fe/unit_tests_prof-fe_szabab_test.$(OBJEXT) \
 	fe/unit_tests_prof-fe_xyz_test.$(OBJEXT) \
 	fe/unit_tests_prof-dual_shape_verification_test.$(OBJEXT) \
+	fe/unit_tests_prof-fe_lagrange_shape_verification_test.$(OBJEXT) \
 	geom/unit_tests_prof-bbox_test.$(OBJEXT) \
 	geom/unit_tests_prof-edge_test.$(OBJEXT) \
 	geom/unit_tests_prof-elem_test.$(OBJEXT) \
@@ -1245,6 +1255,7 @@ am__depfiles_remade = ./$(DEPDIR)/unit_tests_dbg-driver.Po \
 	fe/$(DEPDIR)/unit_tests_dbg-fe_hierarchic_test.Po \
 	fe/$(DEPDIR)/unit_tests_dbg-fe_l2_hierarchic_test.Po \
 	fe/$(DEPDIR)/unit_tests_dbg-fe_l2_lagrange_test.Po \
+	fe/$(DEPDIR)/unit_tests_dbg-fe_lagrange_shape_verification_test.Po \
 	fe/$(DEPDIR)/unit_tests_dbg-fe_lagrange_test.Po \
 	fe/$(DEPDIR)/unit_tests_dbg-fe_monomial_test.Po \
 	fe/$(DEPDIR)/unit_tests_dbg-fe_rational_map.Po \
@@ -1260,6 +1271,7 @@ am__depfiles_remade = ./$(DEPDIR)/unit_tests_dbg-driver.Po \
 	fe/$(DEPDIR)/unit_tests_devel-fe_hierarchic_test.Po \
 	fe/$(DEPDIR)/unit_tests_devel-fe_l2_hierarchic_test.Po \
 	fe/$(DEPDIR)/unit_tests_devel-fe_l2_lagrange_test.Po \
+	fe/$(DEPDIR)/unit_tests_devel-fe_lagrange_shape_verification_test.Po \
 	fe/$(DEPDIR)/unit_tests_devel-fe_lagrange_test.Po \
 	fe/$(DEPDIR)/unit_tests_devel-fe_monomial_test.Po \
 	fe/$(DEPDIR)/unit_tests_devel-fe_rational_map.Po \
@@ -1275,6 +1287,7 @@ am__depfiles_remade = ./$(DEPDIR)/unit_tests_dbg-driver.Po \
 	fe/$(DEPDIR)/unit_tests_oprof-fe_hierarchic_test.Po \
 	fe/$(DEPDIR)/unit_tests_oprof-fe_l2_hierarchic_test.Po \
 	fe/$(DEPDIR)/unit_tests_oprof-fe_l2_lagrange_test.Po \
+	fe/$(DEPDIR)/unit_tests_oprof-fe_lagrange_shape_verification_test.Po \
 	fe/$(DEPDIR)/unit_tests_oprof-fe_lagrange_test.Po \
 	fe/$(DEPDIR)/unit_tests_oprof-fe_monomial_test.Po \
 	fe/$(DEPDIR)/unit_tests_oprof-fe_rational_map.Po \
@@ -1290,6 +1303,7 @@ am__depfiles_remade = ./$(DEPDIR)/unit_tests_dbg-driver.Po \
 	fe/$(DEPDIR)/unit_tests_opt-fe_hierarchic_test.Po \
 	fe/$(DEPDIR)/unit_tests_opt-fe_l2_hierarchic_test.Po \
 	fe/$(DEPDIR)/unit_tests_opt-fe_l2_lagrange_test.Po \
+	fe/$(DEPDIR)/unit_tests_opt-fe_lagrange_shape_verification_test.Po \
 	fe/$(DEPDIR)/unit_tests_opt-fe_lagrange_test.Po \
 	fe/$(DEPDIR)/unit_tests_opt-fe_monomial_test.Po \
 	fe/$(DEPDIR)/unit_tests_opt-fe_rational_map.Po \
@@ -1305,6 +1319,7 @@ am__depfiles_remade = ./$(DEPDIR)/unit_tests_dbg-driver.Po \
 	fe/$(DEPDIR)/unit_tests_prof-fe_hierarchic_test.Po \
 	fe/$(DEPDIR)/unit_tests_prof-fe_l2_hierarchic_test.Po \
 	fe/$(DEPDIR)/unit_tests_prof-fe_l2_lagrange_test.Po \
+	fe/$(DEPDIR)/unit_tests_prof-fe_lagrange_shape_verification_test.Po \
 	fe/$(DEPDIR)/unit_tests_prof-fe_lagrange_test.Po \
 	fe/$(DEPDIR)/unit_tests_prof-fe_monomial_test.Po \
 	fe/$(DEPDIR)/unit_tests_prof-fe_rational_map.Po \
@@ -2270,7 +2285,8 @@ unit_tests_sources = driver.C libmesh_cppunit.h stream_redirector.h \
 	fe/fe_lagrange_test.C fe/fe_monomial_test.C \
 	fe/fe_rational_map.C fe/fe_rational_test.C fe/fe_side_test.C \
 	fe/fe_szabab_test.C fe/fe_test.h fe/fe_xyz_test.C \
-	fe/dual_shape_verification_test.C geom/bbox_test.C \
+	fe/dual_shape_verification_test.C \
+	fe/fe_lagrange_shape_verification_test.C geom/bbox_test.C \
 	geom/edge_test.C geom/elem_test.C geom/elem_test.h \
 	geom/node_test.C geom/point_test.C geom/point_test.h \
 	geom/side_test.C geom/volume_test.C \
@@ -2582,6 +2598,8 @@ fe/unit_tests_dbg-fe_xyz_test.$(OBJEXT): fe/$(am__dirstamp) \
 	fe/$(DEPDIR)/$(am__dirstamp)
 fe/unit_tests_dbg-dual_shape_verification_test.$(OBJEXT):  \
 	fe/$(am__dirstamp) fe/$(DEPDIR)/$(am__dirstamp)
+fe/unit_tests_dbg-fe_lagrange_shape_verification_test.$(OBJEXT):  \
+	fe/$(am__dirstamp) fe/$(DEPDIR)/$(am__dirstamp)
 geom/$(am__dirstamp):
 	@$(MKDIR_P) geom
 	@: >>geom/$(am__dirstamp)
@@ -2890,6 +2908,8 @@ fe/unit_tests_devel-fe_xyz_test.$(OBJEXT): fe/$(am__dirstamp) \
 	fe/$(DEPDIR)/$(am__dirstamp)
 fe/unit_tests_devel-dual_shape_verification_test.$(OBJEXT):  \
 	fe/$(am__dirstamp) fe/$(DEPDIR)/$(am__dirstamp)
+fe/unit_tests_devel-fe_lagrange_shape_verification_test.$(OBJEXT):  \
+	fe/$(am__dirstamp) fe/$(DEPDIR)/$(am__dirstamp)
 geom/unit_tests_devel-bbox_test.$(OBJEXT): geom/$(am__dirstamp) \
 	geom/$(DEPDIR)/$(am__dirstamp)
 geom/unit_tests_devel-edge_test.$(OBJEXT): geom/$(am__dirstamp) \
@@ -3138,6 +3158,8 @@ fe/unit_tests_oprof-fe_xyz_test.$(OBJEXT): fe/$(am__dirstamp) \
 	fe/$(DEPDIR)/$(am__dirstamp)
 fe/unit_tests_oprof-dual_shape_verification_test.$(OBJEXT):  \
 	fe/$(am__dirstamp) fe/$(DEPDIR)/$(am__dirstamp)
+fe/unit_tests_oprof-fe_lagrange_shape_verification_test.$(OBJEXT):  \
+	fe/$(am__dirstamp) fe/$(DEPDIR)/$(am__dirstamp)
 geom/unit_tests_oprof-bbox_test.$(OBJEXT): geom/$(am__dirstamp) \
 	geom/$(DEPDIR)/$(am__dirstamp)
 geom/unit_tests_oprof-edge_test.$(OBJEXT): geom/$(am__dirstamp) \
@@ -3386,6 +3408,8 @@ fe/unit_tests_opt-fe_xyz_test.$(OBJEXT): fe/$(am__dirstamp) \
 	fe/$(DEPDIR)/$(am__dirstamp)
 fe/unit_tests_opt-dual_shape_verification_test.$(OBJEXT):  \
 	fe/$(am__dirstamp) fe/$(DEPDIR)/$(am__dirstamp)
+fe/unit_tests_opt-fe_lagrange_shape_verification_test.$(OBJEXT):  \
+	fe/$(am__dirstamp) fe/$(DEPDIR)/$(am__dirstamp)
 geom/unit_tests_opt-bbox_test.$(OBJEXT): geom/$(am__dirstamp) \
 	geom/$(DEPDIR)/$(am__dirstamp)
 geom/unit_tests_opt-edge_test.$(OBJEXT): geom/$(am__dirstamp) \
@@ -3634,6 +3658,8 @@ fe/unit_tests_prof-fe_xyz_test.$(OBJEXT): fe/$(am__dirstamp) \
 	fe/$(DEPDIR)/$(am__dirstamp)
 fe/unit_tests_prof-dual_shape_verification_test.$(OBJEXT):  \
 	fe/$(am__dirstamp) fe/$(DEPDIR)/$(am__dirstamp)
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+	fe/$(am__dirstamp) fe/$(DEPDIR)/$(am__dirstamp)
 geom/unit_tests_prof-bbox_test.$(OBJEXT): geom/$(am__dirstamp) \
 	geom/$(DEPDIR)/$(am__dirstamp)
 geom/unit_tests_prof-edge_test.$(OBJEXT): geom/$(am__dirstamp) \
@@ -3904,6 +3930,7 @@ distclean-compile:
 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_dbg-fe_hierarchic_test.Po@am__quote@ # am--include-marker
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 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_dbg-fe_l2_lagrange_test.Po@am__quote@ # am--include-marker
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 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_dbg-fe_rational_map.Po@am__quote@ # am--include-marker
@@ -3919,6 +3946,7 @@ distclean-compile:
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 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_devel-fe_l2_hierarchic_test.Po@am__quote@ # am--include-marker
 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_devel-fe_l2_lagrange_test.Po@am__quote@ # am--include-marker
+@AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_devel-fe_lagrange_shape_verification_test.Po@am__quote@ # am--include-marker
 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_devel-fe_lagrange_test.Po@am__quote@ # am--include-marker
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 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_devel-fe_rational_map.Po@am__quote@ # am--include-marker
@@ -3934,6 +3962,7 @@ distclean-compile:
 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_oprof-fe_hierarchic_test.Po@am__quote@ # am--include-marker
 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_oprof-fe_l2_hierarchic_test.Po@am__quote@ # am--include-marker
 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_oprof-fe_l2_lagrange_test.Po@am__quote@ # am--include-marker
+@AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_oprof-fe_lagrange_shape_verification_test.Po@am__quote@ # am--include-marker
 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_oprof-fe_lagrange_test.Po@am__quote@ # am--include-marker
 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_oprof-fe_monomial_test.Po@am__quote@ # am--include-marker
 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_oprof-fe_rational_map.Po@am__quote@ # am--include-marker
@@ -3949,6 +3978,7 @@ distclean-compile:
 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_opt-fe_hierarchic_test.Po@am__quote@ # am--include-marker
 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_opt-fe_l2_hierarchic_test.Po@am__quote@ # am--include-marker
 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_opt-fe_l2_lagrange_test.Po@am__quote@ # am--include-marker
+@AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_opt-fe_lagrange_shape_verification_test.Po@am__quote@ # am--include-marker
 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_opt-fe_lagrange_test.Po@am__quote@ # am--include-marker
 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_opt-fe_monomial_test.Po@am__quote@ # am--include-marker
 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_opt-fe_rational_map.Po@am__quote@ # am--include-marker
@@ -3964,6 +3994,7 @@ distclean-compile:
 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_prof-fe_hierarchic_test.Po@am__quote@ # am--include-marker
 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_prof-fe_l2_hierarchic_test.Po@am__quote@ # am--include-marker
 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_prof-fe_l2_lagrange_test.Po@am__quote@ # am--include-marker
+@AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_prof-fe_lagrange_shape_verification_test.Po@am__quote@ # am--include-marker
 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_prof-fe_lagrange_test.Po@am__quote@ # am--include-marker
 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_prof-fe_monomial_test.Po@am__quote@ # am--include-marker
 @AMDEP_TRUE@@am__include@ @am__quote@fe/$(DEPDIR)/unit_tests_prof-fe_rational_map.Po@am__quote@ # am--include-marker
@@ -4805,6 +4836,20 @@ fe/unit_tests_dbg-dual_shape_verification_test.obj: fe/dual_shape_verification_t
 @AMDEP_TRUE@@am__fastdepCXX_FALSE@	DEPDIR=$(DEPDIR) $(CXXDEPMODE) $(depcomp) @AMDEPBACKSLASH@
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+fe/unit_tests_dbg-fe_lagrange_shape_verification_test.o: fe/fe_lagrange_shape_verification_test.C
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+
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+
 geom/unit_tests_dbg-bbox_test.o: geom/bbox_test.C
 @am__fastdepCXX_TRUE@	$(AM_V_CXX)$(CXX) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(unit_tests_dbg_CPPFLAGS) $(CPPFLAGS) $(unit_tests_dbg_CXXFLAGS) $(CXXFLAGS) -MT geom/unit_tests_dbg-bbox_test.o -MD -MP -MF geom/$(DEPDIR)/unit_tests_dbg-bbox_test.Tpo -c -o geom/unit_tests_dbg-bbox_test.o `test -f 'geom/bbox_test.C' || echo '$(srcdir)/'`geom/bbox_test.C
 @am__fastdepCXX_TRUE@	$(AM_V_at)$(am__mv) geom/$(DEPDIR)/unit_tests_dbg-bbox_test.Tpo geom/$(DEPDIR)/unit_tests_dbg-bbox_test.Po
@@ -6471,6 +6516,20 @@ fe/unit_tests_devel-dual_shape_verification_test.obj: fe/dual_shape_verification
 @AMDEP_TRUE@@am__fastdepCXX_FALSE@	DEPDIR=$(DEPDIR) $(CXXDEPMODE) $(depcomp) @AMDEPBACKSLASH@
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+fe/unit_tests_devel-fe_lagrange_shape_verification_test.o: fe/fe_lagrange_shape_verification_test.C
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+
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+
 geom/unit_tests_devel-bbox_test.o: geom/bbox_test.C
 @am__fastdepCXX_TRUE@	$(AM_V_CXX)$(CXX) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(unit_tests_devel_CPPFLAGS) $(CPPFLAGS) $(unit_tests_devel_CXXFLAGS) $(CXXFLAGS) -MT geom/unit_tests_devel-bbox_test.o -MD -MP -MF geom/$(DEPDIR)/unit_tests_devel-bbox_test.Tpo -c -o geom/unit_tests_devel-bbox_test.o `test -f 'geom/bbox_test.C' || echo '$(srcdir)/'`geom/bbox_test.C
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@@ -8137,6 +8196,20 @@ fe/unit_tests_oprof-dual_shape_verification_test.obj: fe/dual_shape_verification
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+fe/unit_tests_oprof-fe_lagrange_shape_verification_test.o: fe/fe_lagrange_shape_verification_test.C
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+
+fe/unit_tests_oprof-fe_lagrange_shape_verification_test.obj: fe/fe_lagrange_shape_verification_test.C
+@am__fastdepCXX_TRUE@	$(AM_V_CXX)$(CXX) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(unit_tests_oprof_CPPFLAGS) $(CPPFLAGS) $(unit_tests_oprof_CXXFLAGS) $(CXXFLAGS) -MT fe/unit_tests_oprof-fe_lagrange_shape_verification_test.obj -MD -MP -MF fe/$(DEPDIR)/unit_tests_oprof-fe_lagrange_shape_verification_test.Tpo -c -o fe/unit_tests_oprof-fe_lagrange_shape_verification_test.obj `if test -f 'fe/fe_lagrange_shape_verification_test.C'; then $(CYGPATH_W) 'fe/fe_lagrange_shape_verification_test.C'; else $(CYGPATH_W) '$(srcdir)/fe/fe_lagrange_shape_verification_test.C'; fi`
+@am__fastdepCXX_TRUE@	$(AM_V_at)$(am__mv) fe/$(DEPDIR)/unit_tests_oprof-fe_lagrange_shape_verification_test.Tpo fe/$(DEPDIR)/unit_tests_oprof-fe_lagrange_shape_verification_test.Po
+@AMDEP_TRUE@@am__fastdepCXX_FALSE@	$(AM_V_CXX)source='fe/fe_lagrange_shape_verification_test.C' object='fe/unit_tests_oprof-fe_lagrange_shape_verification_test.obj' libtool=no @AMDEPBACKSLASH@
+@AMDEP_TRUE@@am__fastdepCXX_FALSE@	DEPDIR=$(DEPDIR) $(CXXDEPMODE) $(depcomp) @AMDEPBACKSLASH@
+@am__fastdepCXX_FALSE@	$(AM_V_CXX@am__nodep@)$(CXX) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(unit_tests_oprof_CPPFLAGS) $(CPPFLAGS) $(unit_tests_oprof_CXXFLAGS) $(CXXFLAGS) -c -o fe/unit_tests_oprof-fe_lagrange_shape_verification_test.obj `if test -f 'fe/fe_lagrange_shape_verification_test.C'; then $(CYGPATH_W) 'fe/fe_lagrange_shape_verification_test.C'; else $(CYGPATH_W) '$(srcdir)/fe/fe_lagrange_shape_verification_test.C'; fi`
+
 geom/unit_tests_oprof-bbox_test.o: geom/bbox_test.C
 @am__fastdepCXX_TRUE@	$(AM_V_CXX)$(CXX) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(unit_tests_oprof_CPPFLAGS) $(CPPFLAGS) $(unit_tests_oprof_CXXFLAGS) $(CXXFLAGS) -MT geom/unit_tests_oprof-bbox_test.o -MD -MP -MF geom/$(DEPDIR)/unit_tests_oprof-bbox_test.Tpo -c -o geom/unit_tests_oprof-bbox_test.o `test -f 'geom/bbox_test.C' || echo '$(srcdir)/'`geom/bbox_test.C
 @am__fastdepCXX_TRUE@	$(AM_V_at)$(am__mv) geom/$(DEPDIR)/unit_tests_oprof-bbox_test.Tpo geom/$(DEPDIR)/unit_tests_oprof-bbox_test.Po
@@ -9803,6 +9876,20 @@ fe/unit_tests_opt-dual_shape_verification_test.obj: fe/dual_shape_verification_t
 @AMDEP_TRUE@@am__fastdepCXX_FALSE@	DEPDIR=$(DEPDIR) $(CXXDEPMODE) $(depcomp) @AMDEPBACKSLASH@
 @am__fastdepCXX_FALSE@	$(AM_V_CXX@am__nodep@)$(CXX) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(unit_tests_opt_CPPFLAGS) $(CPPFLAGS) $(unit_tests_opt_CXXFLAGS) $(CXXFLAGS) -c -o fe/unit_tests_opt-dual_shape_verification_test.obj `if test -f 'fe/dual_shape_verification_test.C'; then $(CYGPATH_W) 'fe/dual_shape_verification_test.C'; else $(CYGPATH_W) '$(srcdir)/fe/dual_shape_verification_test.C'; fi`
 
+fe/unit_tests_opt-fe_lagrange_shape_verification_test.o: fe/fe_lagrange_shape_verification_test.C
+@am__fastdepCXX_TRUE@	$(AM_V_CXX)$(CXX) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(unit_tests_opt_CPPFLAGS) $(CPPFLAGS) $(unit_tests_opt_CXXFLAGS) $(CXXFLAGS) -MT fe/unit_tests_opt-fe_lagrange_shape_verification_test.o -MD -MP -MF fe/$(DEPDIR)/unit_tests_opt-fe_lagrange_shape_verification_test.Tpo -c -o fe/unit_tests_opt-fe_lagrange_shape_verification_test.o `test -f 'fe/fe_lagrange_shape_verification_test.C' || echo '$(srcdir)/'`fe/fe_lagrange_shape_verification_test.C
+@am__fastdepCXX_TRUE@	$(AM_V_at)$(am__mv) fe/$(DEPDIR)/unit_tests_opt-fe_lagrange_shape_verification_test.Tpo fe/$(DEPDIR)/unit_tests_opt-fe_lagrange_shape_verification_test.Po
+@AMDEP_TRUE@@am__fastdepCXX_FALSE@	$(AM_V_CXX)source='fe/fe_lagrange_shape_verification_test.C' object='fe/unit_tests_opt-fe_lagrange_shape_verification_test.o' libtool=no @AMDEPBACKSLASH@
+@AMDEP_TRUE@@am__fastdepCXX_FALSE@	DEPDIR=$(DEPDIR) $(CXXDEPMODE) $(depcomp) @AMDEPBACKSLASH@
+@am__fastdepCXX_FALSE@	$(AM_V_CXX@am__nodep@)$(CXX) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(unit_tests_opt_CPPFLAGS) $(CPPFLAGS) $(unit_tests_opt_CXXFLAGS) $(CXXFLAGS) -c -o fe/unit_tests_opt-fe_lagrange_shape_verification_test.o `test -f 'fe/fe_lagrange_shape_verification_test.C' || echo '$(srcdir)/'`fe/fe_lagrange_shape_verification_test.C
+
+fe/unit_tests_opt-fe_lagrange_shape_verification_test.obj: fe/fe_lagrange_shape_verification_test.C
+@am__fastdepCXX_TRUE@	$(AM_V_CXX)$(CXX) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(unit_tests_opt_CPPFLAGS) $(CPPFLAGS) $(unit_tests_opt_CXXFLAGS) $(CXXFLAGS) -MT fe/unit_tests_opt-fe_lagrange_shape_verification_test.obj -MD -MP -MF fe/$(DEPDIR)/unit_tests_opt-fe_lagrange_shape_verification_test.Tpo -c -o fe/unit_tests_opt-fe_lagrange_shape_verification_test.obj `if test -f 'fe/fe_lagrange_shape_verification_test.C'; then $(CYGPATH_W) 'fe/fe_lagrange_shape_verification_test.C'; else $(CYGPATH_W) '$(srcdir)/fe/fe_lagrange_shape_verification_test.C'; fi`
+@am__fastdepCXX_TRUE@	$(AM_V_at)$(am__mv) fe/$(DEPDIR)/unit_tests_opt-fe_lagrange_shape_verification_test.Tpo fe/$(DEPDIR)/unit_tests_opt-fe_lagrange_shape_verification_test.Po
+@AMDEP_TRUE@@am__fastdepCXX_FALSE@	$(AM_V_CXX)source='fe/fe_lagrange_shape_verification_test.C' object='fe/unit_tests_opt-fe_lagrange_shape_verification_test.obj' libtool=no @AMDEPBACKSLASH@
+@AMDEP_TRUE@@am__fastdepCXX_FALSE@	DEPDIR=$(DEPDIR) $(CXXDEPMODE) $(depcomp) @AMDEPBACKSLASH@
+@am__fastdepCXX_FALSE@	$(AM_V_CXX@am__nodep@)$(CXX) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(unit_tests_opt_CPPFLAGS) $(CPPFLAGS) $(unit_tests_opt_CXXFLAGS) $(CXXFLAGS) -c -o fe/unit_tests_opt-fe_lagrange_shape_verification_test.obj `if test -f 'fe/fe_lagrange_shape_verification_test.C'; then $(CYGPATH_W) 'fe/fe_lagrange_shape_verification_test.C'; else $(CYGPATH_W) '$(srcdir)/fe/fe_lagrange_shape_verification_test.C'; fi`
+
 geom/unit_tests_opt-bbox_test.o: geom/bbox_test.C
 @am__fastdepCXX_TRUE@	$(AM_V_CXX)$(CXX) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(unit_tests_opt_CPPFLAGS) $(CPPFLAGS) $(unit_tests_opt_CXXFLAGS) $(CXXFLAGS) -MT geom/unit_tests_opt-bbox_test.o -MD -MP -MF geom/$(DEPDIR)/unit_tests_opt-bbox_test.Tpo -c -o geom/unit_tests_opt-bbox_test.o `test -f 'geom/bbox_test.C' || echo '$(srcdir)/'`geom/bbox_test.C
 @am__fastdepCXX_TRUE@	$(AM_V_at)$(am__mv) geom/$(DEPDIR)/unit_tests_opt-bbox_test.Tpo geom/$(DEPDIR)/unit_tests_opt-bbox_test.Po
@@ -11469,6 +11556,20 @@ fe/unit_tests_prof-dual_shape_verification_test.obj: fe/dual_shape_verification_
 @AMDEP_TRUE@@am__fastdepCXX_FALSE@	DEPDIR=$(DEPDIR) $(CXXDEPMODE) $(depcomp) @AMDEPBACKSLASH@
 @am__fastdepCXX_FALSE@	$(AM_V_CXX@am__nodep@)$(CXX) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(unit_tests_prof_CPPFLAGS) $(CPPFLAGS) $(unit_tests_prof_CXXFLAGS) $(CXXFLAGS) -c -o fe/unit_tests_prof-dual_shape_verification_test.obj `if test -f 'fe/dual_shape_verification_test.C'; then $(CYGPATH_W) 'fe/dual_shape_verification_test.C'; else $(CYGPATH_W) '$(srcdir)/fe/dual_shape_verification_test.C'; fi`
 
+fe/unit_tests_prof-fe_lagrange_shape_verification_test.o: fe/fe_lagrange_shape_verification_test.C
+@am__fastdepCXX_TRUE@	$(AM_V_CXX)$(CXX) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(unit_tests_prof_CPPFLAGS) $(CPPFLAGS) $(unit_tests_prof_CXXFLAGS) $(CXXFLAGS) -MT fe/unit_tests_prof-fe_lagrange_shape_verification_test.o -MD -MP -MF fe/$(DEPDIR)/unit_tests_prof-fe_lagrange_shape_verification_test.Tpo -c -o fe/unit_tests_prof-fe_lagrange_shape_verification_test.o `test -f 'fe/fe_lagrange_shape_verification_test.C' || echo '$(srcdir)/'`fe/fe_lagrange_shape_verification_test.C
+@am__fastdepCXX_TRUE@	$(AM_V_at)$(am__mv) fe/$(DEPDIR)/unit_tests_prof-fe_lagrange_shape_verification_test.Tpo fe/$(DEPDIR)/unit_tests_prof-fe_lagrange_shape_verification_test.Po
+@AMDEP_TRUE@@am__fastdepCXX_FALSE@	$(AM_V_CXX)source='fe/fe_lagrange_shape_verification_test.C' object='fe/unit_tests_prof-fe_lagrange_shape_verification_test.o' libtool=no @AMDEPBACKSLASH@
+@AMDEP_TRUE@@am__fastdepCXX_FALSE@	DEPDIR=$(DEPDIR) $(CXXDEPMODE) $(depcomp) @AMDEPBACKSLASH@
+@am__fastdepCXX_FALSE@	$(AM_V_CXX@am__nodep@)$(CXX) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(unit_tests_prof_CPPFLAGS) $(CPPFLAGS) $(unit_tests_prof_CXXFLAGS) $(CXXFLAGS) -c -o fe/unit_tests_prof-fe_lagrange_shape_verification_test.o `test -f 'fe/fe_lagrange_shape_verification_test.C' || echo '$(srcdir)/'`fe/fe_lagrange_shape_verification_test.C
+
+fe/unit_tests_prof-fe_lagrange_shape_verification_test.obj: fe/fe_lagrange_shape_verification_test.C
+@am__fastdepCXX_TRUE@	$(AM_V_CXX)$(CXX) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(unit_tests_prof_CPPFLAGS) $(CPPFLAGS) $(unit_tests_prof_CXXFLAGS) $(CXXFLAGS) -MT fe/unit_tests_prof-fe_lagrange_shape_verification_test.obj -MD -MP -MF fe/$(DEPDIR)/unit_tests_prof-fe_lagrange_shape_verification_test.Tpo -c -o fe/unit_tests_prof-fe_lagrange_shape_verification_test.obj `if test -f 'fe/fe_lagrange_shape_verification_test.C'; then $(CYGPATH_W) 'fe/fe_lagrange_shape_verification_test.C'; else $(CYGPATH_W) '$(srcdir)/fe/fe_lagrange_shape_verification_test.C'; fi`
+@am__fastdepCXX_TRUE@	$(AM_V_at)$(am__mv) fe/$(DEPDIR)/unit_tests_prof-fe_lagrange_shape_verification_test.Tpo fe/$(DEPDIR)/unit_tests_prof-fe_lagrange_shape_verification_test.Po
+@AMDEP_TRUE@@am__fastdepCXX_FALSE@	$(AM_V_CXX)source='fe/fe_lagrange_shape_verification_test.C' object='fe/unit_tests_prof-fe_lagrange_shape_verification_test.obj' libtool=no @AMDEPBACKSLASH@
+@AMDEP_TRUE@@am__fastdepCXX_FALSE@	DEPDIR=$(DEPDIR) $(CXXDEPMODE) $(depcomp) @AMDEPBACKSLASH@
+@am__fastdepCXX_FALSE@	$(AM_V_CXX@am__nodep@)$(CXX) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(unit_tests_prof_CPPFLAGS) $(CPPFLAGS) $(unit_tests_prof_CXXFLAGS) $(CXXFLAGS) -c -o fe/unit_tests_prof-fe_lagrange_shape_verification_test.obj `if test -f 'fe/fe_lagrange_shape_verification_test.C'; then $(CYGPATH_W) 'fe/fe_lagrange_shape_verification_test.C'; else $(CYGPATH_W) '$(srcdir)/fe/fe_lagrange_shape_verification_test.C'; fi`
+
 geom/unit_tests_prof-bbox_test.o: geom/bbox_test.C
 @am__fastdepCXX_TRUE@	$(AM_V_CXX)$(CXX) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(unit_tests_prof_CPPFLAGS) $(CPPFLAGS) $(unit_tests_prof_CXXFLAGS) $(CXXFLAGS) -MT geom/unit_tests_prof-bbox_test.o -MD -MP -MF geom/$(DEPDIR)/unit_tests_prof-bbox_test.Tpo -c -o geom/unit_tests_prof-bbox_test.o `test -f 'geom/bbox_test.C' || echo '$(srcdir)/'`geom/bbox_test.C
 @am__fastdepCXX_TRUE@	$(AM_V_at)$(am__mv) geom/$(DEPDIR)/unit_tests_prof-bbox_test.Tpo geom/$(DEPDIR)/unit_tests_prof-bbox_test.Po
@@ -13223,6 +13324,7 @@ distclean: distclean-am
 	-rm -f fe/$(DEPDIR)/unit_tests_dbg-fe_hierarchic_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_dbg-fe_l2_hierarchic_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_dbg-fe_l2_lagrange_test.Po
+	-rm -f fe/$(DEPDIR)/unit_tests_dbg-fe_lagrange_shape_verification_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_dbg-fe_lagrange_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_dbg-fe_monomial_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_dbg-fe_rational_map.Po
@@ -13238,6 +13340,7 @@ distclean: distclean-am
 	-rm -f fe/$(DEPDIR)/unit_tests_devel-fe_hierarchic_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_devel-fe_l2_hierarchic_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_devel-fe_l2_lagrange_test.Po
+	-rm -f fe/$(DEPDIR)/unit_tests_devel-fe_lagrange_shape_verification_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_devel-fe_lagrange_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_devel-fe_monomial_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_devel-fe_rational_map.Po
@@ -13253,6 +13356,7 @@ distclean: distclean-am
 	-rm -f fe/$(DEPDIR)/unit_tests_oprof-fe_hierarchic_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_oprof-fe_l2_hierarchic_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_oprof-fe_l2_lagrange_test.Po
+	-rm -f fe/$(DEPDIR)/unit_tests_oprof-fe_lagrange_shape_verification_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_oprof-fe_lagrange_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_oprof-fe_monomial_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_oprof-fe_rational_map.Po
@@ -13268,6 +13372,7 @@ distclean: distclean-am
 	-rm -f fe/$(DEPDIR)/unit_tests_opt-fe_hierarchic_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_opt-fe_l2_hierarchic_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_opt-fe_l2_lagrange_test.Po
+	-rm -f fe/$(DEPDIR)/unit_tests_opt-fe_lagrange_shape_verification_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_opt-fe_lagrange_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_opt-fe_monomial_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_opt-fe_rational_map.Po
@@ -13283,6 +13388,7 @@ distclean: distclean-am
 	-rm -f fe/$(DEPDIR)/unit_tests_prof-fe_hierarchic_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_prof-fe_l2_hierarchic_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_prof-fe_l2_lagrange_test.Po
+	-rm -f fe/$(DEPDIR)/unit_tests_prof-fe_lagrange_shape_verification_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_prof-fe_lagrange_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_prof-fe_monomial_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_prof-fe_rational_map.Po
@@ -13865,6 +13971,7 @@ maintainer-clean: maintainer-clean-am
 	-rm -f fe/$(DEPDIR)/unit_tests_dbg-fe_hierarchic_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_dbg-fe_l2_hierarchic_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_dbg-fe_l2_lagrange_test.Po
+	-rm -f fe/$(DEPDIR)/unit_tests_dbg-fe_lagrange_shape_verification_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_dbg-fe_lagrange_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_dbg-fe_monomial_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_dbg-fe_rational_map.Po
@@ -13880,6 +13987,7 @@ maintainer-clean: maintainer-clean-am
 	-rm -f fe/$(DEPDIR)/unit_tests_devel-fe_hierarchic_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_devel-fe_l2_hierarchic_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_devel-fe_l2_lagrange_test.Po
+	-rm -f fe/$(DEPDIR)/unit_tests_devel-fe_lagrange_shape_verification_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_devel-fe_lagrange_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_devel-fe_monomial_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_devel-fe_rational_map.Po
@@ -13895,6 +14003,7 @@ maintainer-clean: maintainer-clean-am
 	-rm -f fe/$(DEPDIR)/unit_tests_oprof-fe_hierarchic_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_oprof-fe_l2_hierarchic_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_oprof-fe_l2_lagrange_test.Po
+	-rm -f fe/$(DEPDIR)/unit_tests_oprof-fe_lagrange_shape_verification_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_oprof-fe_lagrange_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_oprof-fe_monomial_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_oprof-fe_rational_map.Po
@@ -13910,6 +14019,7 @@ maintainer-clean: maintainer-clean-am
 	-rm -f fe/$(DEPDIR)/unit_tests_opt-fe_hierarchic_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_opt-fe_l2_hierarchic_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_opt-fe_l2_lagrange_test.Po
+	-rm -f fe/$(DEPDIR)/unit_tests_opt-fe_lagrange_shape_verification_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_opt-fe_lagrange_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_opt-fe_monomial_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_opt-fe_rational_map.Po
@@ -13925,6 +14035,7 @@ maintainer-clean: maintainer-clean-am
 	-rm -f fe/$(DEPDIR)/unit_tests_prof-fe_hierarchic_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_prof-fe_l2_hierarchic_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_prof-fe_l2_lagrange_test.Po
+	-rm -f fe/$(DEPDIR)/unit_tests_prof-fe_lagrange_shape_verification_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_prof-fe_lagrange_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_prof-fe_monomial_test.Po
 	-rm -f fe/$(DEPDIR)/unit_tests_prof-fe_rational_map.Po
diff --git a/tests/fe/fe_lagrange_shape_verification_test.C b/tests/fe/fe_lagrange_shape_verification_test.C
new file mode 100644
index 00000000000..76b4d8401a8
--- /dev/null
+++ b/tests/fe/fe_lagrange_shape_verification_test.C
@@ -0,0 +1,61 @@
+// libmesh includes
+#include "libmesh/libmesh.h"
+#include "libmesh/elem.h"
+#include "libmesh/fe.h"
+#include "libmesh/fe_lagrange_shape_1D.h"
+
+// unit test includes
+#include "test_comm.h"
+
+#include "libmesh_cppunit.h"
+
+using namespace libMesh;
+
+/**
+ * This class is for unit testing lagrange shape function values and derivatives
+ */
+class LagrangeShapeTest : public CppUnit::TestCase
+{
+public:
+
+  LIBMESH_CPPUNIT_TEST_SUITE( LagrangeShapeTest );
+  CPPUNIT_TEST( test1DLagrange );
+  CPPUNIT_TEST_SUITE_END();
+
+public:
+
+  void test1DLagrange ()
+  {
+    LOG_UNIT_TEST;
+
+    Real tol = TOLERANCE*TOLERANCE;
+
+    for (auto xi : {0., 1./3., -.5, -1./7.})
+      for(auto o : make_range(1, 4))
+        for(auto i : make_range(o + 1))
+        {
+          LIBMESH_ASSERT_FP_EQUAL(fe_lagrange_1D_shape(Order(o), i, xi),
+                                  fe_lagrange_1D_any_shape(Order(o), i, xi), tol);
+          LIBMESH_ASSERT_FP_EQUAL(fe_lagrange_1D_shape_deriv(Order(o), i, 0, xi),
+                                  fe_lagrange_1D_any_shape_deriv(Order(o), i, 0, xi), tol);
+          LIBMESH_ASSERT_FP_EQUAL(fe_lagrange_1D_shape_second_deriv(Order(o), i, 0, xi),
+                                  fe_lagrange_1D_any_shape_second_deriv(Order(o), i, 0, xi), tol);
+        }
+
+    for (auto xi : {0., 1./3., -.5, -1./7.})
+      for(auto o : make_range(4, 7))
+        for(auto i : make_range(o + 1))
+        {
+          using T = FE<1,LAGRANGE>;
+          const unsigned ii = i == 0 ? 1 : i == 1 ? 0 : o + 2 - i;
+          LIBMESH_ASSERT_FP_EQUAL(T::shape(EDGE3, Order(o), i, xi),
+                                  T::shape(EDGE3, Order(o), ii, -xi), tol);
+          LIBMESH_ASSERT_FP_EQUAL( T::shape_deriv(EDGE3, Order(o), i, 0, xi),
+                                  -T::shape_deriv(EDGE3, Order(o), ii, 0, -xi), tol);
+          LIBMESH_ASSERT_FP_EQUAL(T::shape_second_deriv(EDGE3, Order(o), i, 0, xi),
+                                  T::shape_second_deriv(EDGE3, Order(o), ii, 0, -xi), tol);
+        }
+  }
+};
+
+CPPUNIT_TEST_SUITE_REGISTRATION( LagrangeShapeTest );