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Fix some miscellaneous typos. #13803

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May 24, 2022
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Fix some miscellaneous typos. #13803

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2 changes: 1 addition & 1 deletion examples/step-12/step-12.cc
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Original file line number Diff line number Diff line change
Expand Up @@ -134,7 +134,7 @@ namespace Step12
//
// The following objects are the scratch and copy objects we use in the call
// to MeshWorker::mesh_loop(). The new object is the FEInterfaceValues object,
// that works similar to FEValues or FEFacesValues, except that it acts on
// that works similar to FEValues or FEFaceValues, except that it acts on
// an interface between two cells and allows us to assemble the interface
// terms in our weak form.

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21 changes: 11 additions & 10 deletions include/deal.II/fe/fe_simplex_p_bubbles.h
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Expand Up @@ -25,7 +25,8 @@
DEAL_II_NAMESPACE_OPEN

/**
* @brief Enriched version of FE_P that can be used with nodal quadrature.
* @brief Enriched version of FE_SimplexP that can be used with nodal
* quadrature.
*
* Many explicit time integration schemes require solving a mass matrix at
* each time step. There are various ways around this requirement - for
Expand All @@ -40,18 +41,18 @@ DEAL_II_NAMESPACE_OPEN
* cannot be used with nodal quadrature since some of the quadrature weights
* end up being either zero or negative, resulting in either an unsolvable or
* unstable approximation to the mass matrix. For example: the shape functions
* of FE_P<2>(2) with support points at vertices have mean values of zero so
* that element cannot be used with mass lumping.
* of FE_SimplexP<2>(2) with support points at vertices have mean values of
* zero so that element cannot be used with mass lumping.
* This element avoids this issue by replacing the shape functions of FE_P
* with an augmented space amendable to the construction of nodal quadrature
* rules. For example, on the triangle a single basis function is added
* corresponding to interpolation at the centroid (and all other basis
* This element avoids this issue by replacing the shape functions of
* FE_SimplexP with an augmented space amenable to the construction of nodal
* quadrature rules. For example, on the triangle a single basis function is
* added corresponding to interpolation at the centroid (and all other basis
* functions are updated to preserve the partition of unity property). This
* results in shape functions with positive means (i.e., a valid nodal
* quadrature formula). Similarly, in 3D, the polynomial space of FE_P<3>(2)
* is enriched with five additional degrees of freedom (where four have
* support points at face centroids and one has a support point at the
* quadrature formula). Similarly, in 3D, the polynomial space of
* FE_SimplexP<3>(2) is enriched with five additional degrees of freedom (where
* four have support points at face centroids and one has a support point at the
* centroid) to enable construction of valid nodal quadrature rule.
*
* Since this FE space includes bubbles (i.e., extra functions which are
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