Add CI test

Author: Steve

test/test_parabolic_2d.jl

@@ -321,6 +321,21 @@ end
     end
 end
 
+@trixi_testset "TreeMesh2D: elixir_advection_diffusion_implicit_sparse_jacobian.jl" begin
+    @test_trixi_include(joinpath(examples_dir(), "tree_2d_dgsem",
+                                 "elixir_advection_diffusion_implicit_sparse_jacobian.jl"),
+                        initial_refinement_level=4, tspan=(0.0, 0.4), polydeg=3,
+                        l2=[4.3996570276332366e-5], linf=[7.656808122324943e-5])
+    # Ensure that we do not have excessive memory allocations
+    # (e.g., from type instabilities)
+    let
+        t = sol.t[end]
+        u_ode = sol.u[end]
+        du_ode = similar(u_ode)
+        @test (@allocated Trixi.rhs!(du_ode, u_ode, semi_float_type, t)) < 1000
+    end
+end
+
 @trixi_testset "TreeMesh2D: elixir_navierstokes_convergence.jl" begin
     @test_trixi_include(joinpath(examples_dir(), "tree_2d_dgsem",
                                  "elixir_navierstokes_convergence.jl"),