@@ -31,10 +31,10 @@ a few points.
3131 # evaluate f at one 2-dimensional point
3232 f.at([0.2, 0.4])
3333
34- # evaluate f at two 2-dimensional point
34+ # evaluate f at two 2-dimensional points
3535 f.at([0.2, 0.4], [1.2, 0.5])
3636
37- # evaluate f at two 2-dimensional point (same as above)
37+ # evaluate f at two 2-dimensional points (same as above)
3838 f.at([[0.2, 0.4], [1.2, 0.5]])
3939
4040 While in these examples we have only shown lists, other *iterables *
@@ -210,15 +210,15 @@ by rank B then they will be moved to rank B.
210210
211211If the same coordinates are supplied more than once, they are always assumed to
212212be a new vertex: this is true for both ``redundant = True `` and
213- ``redunant = False ``. So if we have the same set of points on all MPI processes
213+ ``redundant = False ``. So if we have the same set of points on all MPI processes
214214and switch from ``redundant = True `` to ``redundant = False `` we will get point
215215duplication.
216216
217217
218218Points outside the domain
219219~~~~~~~~~~~~~~~~~~~~~~~~~
220220
221- Be default points outside the domain by more than the :ref: `specified
221+ By default points outside the domain by more than the :ref: `specified
222222tolerance <tolerance>` will generate
223223a :class: `~.VertexOnlyMeshMissingPointsError `. This can be switched to a
224224warning or switched off entirely:
@@ -262,7 +262,7 @@ These equivalent expressions for point evaluation
262262
263263 where :math: `N` is the number of points, :math: `x_i` is the :math: `i`\t h point,
264264:math: `\Omega ` is a 'parent' mesh, :math: `f` is a function on that mesh,
265- :math: `\delta ` is a dirac delta distribition can therefore be written in
265+ :math: `\delta ` is a Dirac delta distribution can therefore be written in
266266Firedrake using :func: `~.VertexOnlyMesh ` and :func: `~.interpolate ` as
267267
268268.. literalinclude :: ../../tests/firedrake/vertexonly/test_vertex_only_manual.py
@@ -320,7 +320,7 @@ distributed** we can use :py:attr:`~.VertexOnlyMeshTopology.input_ordering` as f
320320
321321.. note ::
322322
323- When a a vertex-only mesh is created with ``redundant = True `` (which is the
323+ When a vertex-only mesh is created with ``redundant = True `` (which is the
324324 default when creating a :func: `~.VertexOnlyMesh `) the
325325 :py:attr: `~.VertexOnlyMeshTopology.input_ordering ` method will return a vertex-only
326326 mesh with all points on rank 0.
@@ -331,7 +331,7 @@ If we ran the example in parallel, the above code would print
331331print ``[0.02, 0.08, 0.18] `` on all ranks and we would have point duplication.
332332
333333If any of the specified points were not found in the mesh, the value on the
334- input ordering vertex-only mesh will not be effected by the interpolation from
334+ input ordering vertex-only mesh will not be affected by the interpolation from
335335the original vertex-only mesh. In the above example, the values would be zero
336336at those points. To make it more obvious that those points were not found, it's
337337a good idea to set the values to ``nan `` before the interpolation:
@@ -430,7 +430,7 @@ works on any :py:class:`~.ufl.core.expr.Expr`, for example:
430430
431431.. code-block :: python3
432432
433- (f*sin(f)([0.2, 0.4])
433+ (f*sin(f)) ([0.2, 0.4])
434434
435435 will evaluate :math: `f \cdot \sin (f)` at :math: `(0.2 , 0.4 )`.
436436
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