From e85369c89aa476a37781d50540000aba09fa9f48 Mon Sep 17 00:00:00 2001 From: Wolfgang Bangerth Date: Thu, 29 Aug 2019 08:15:44 -0600 Subject: [PATCH] Doc updates in a variety of places. --- doc/doxygen/references.bib | 18 +++++++++++++++ include/deal.II/fe/fe_nothing.h | 4 +++- include/deal.II/fe/fe_p1nc.h | 27 ++++++---------------- include/deal.II/fe/mapping_cartesian.h | 32 +++++++++++++++++++------- 4 files changed, 52 insertions(+), 29 deletions(-) diff --git a/doc/doxygen/references.bib b/doc/doxygen/references.bib index 3a3ee517cf..e458098bb7 100644 --- a/doc/doxygen/references.bib +++ b/doc/doxygen/references.bib @@ -306,3 +306,21 @@ MRREVIEWER = {Jose Luis Gracia}, DOI = {10.1137/070706616}, URL = {http://dx.doi.org/10.1137/070706616}, } + + +% ------------------------------------ +% References used elsewhere +% ------------------------------------ + +@article{park2003p, + title = {P1-nonconforming quadrilateral finite element methods for + second-order elliptic problems}, + author = {Park, Chunjae and Sheen, Dongwoo}, + journal = {SIAM Journal on Numerical Analysis}, + volume = {41}, + number = {2}, + pages = {624--640}, + year = {2003}, + publisher = {SIAM}, + doi = {10.1137/S0036142902404923} +} diff --git a/include/deal.II/fe/fe_nothing.h b/include/deal.II/fe/fe_nothing.h index fd3b8270e6..6861fed40f 100644 --- a/include/deal.II/fe/fe_nothing.h +++ b/include/deal.II/fe/fe_nothing.h @@ -27,7 +27,9 @@ DEAL_II_NAMESPACE_OPEN /*@{*/ /** - * Definition of a finite element with zero degrees of freedom. This class is + * Definition of a finite element space with zero degrees of freedom and that, + * consequently, can only represent a single function: the zero function. + * This class is * useful (in the context of an hp method) to represent empty cells in the * triangulation on which no degrees of freedom should be allocated, or to * describe a field that is extended by zero to a part of the domain where we diff --git a/include/deal.II/fe/fe_p1nc.h b/include/deal.II/fe/fe_p1nc.h index 3d2853e577..7dee6de08d 100644 --- a/include/deal.II/fe/fe_p1nc.h +++ b/include/deal.II/fe/fe_p1nc.h @@ -215,7 +215,7 @@ DEAL_II_NAMESPACE_OPEN * are defined by a cell-wise composition of local shape functions associated * with the node on each element. * - * There is a theoretical result about the linear independency of the global + * There is a theoretical result about the linear independence of the global * basis functions depending on the type of the boundary condition we consider. * * When homogeneous Dirichlet boundary conditions are given, @@ -234,8 +234,8 @@ DEAL_II_NAMESPACE_OPEN * For a smooth function, we construct a piecewise linear function which belongs * to the element space by using its nodal values as DoF values. * - * Note that for the P1 nonconforming element two nodal values of a smooth - * function and its interpolant do not coincide in general, in contrast with + * Note that for the P1 nonconforming element, two nodal values of a smooth + * function and its interpolant do not coincide in general, in contrast to * ordinary Lagrange finite elements. Of course, it is meaningless to refer * 'nodal value' because the element space has nonconformity. But it is also * true even though the single global basis function associated with a node is @@ -249,23 +249,10 @@ DEAL_II_NAMESPACE_OPEN * value 1. This is true whether the quadrilateral is a rectangle, * parallelogram, or any other shape. * - *

References

- * The original paper for the P1 nonconforming element is - * accessible at http://epubs.siam.org/doi/abs/10.1137/S0036142902404923 - * and has the following complete reference: - * @code{.bib} - * @article{park2003p, - * title = {P1-nonconforming quadrilateral finite element methods for - * second-order elliptic problems}, - * author = {Park, Chunjae and Sheen, Dongwoo}, - * journal = {SIAM Journal on Numerical Analysis}, - * volume = {41}, - * number = {2}, - * pages = {624--640}, - * year = {2003}, - * publisher = {SIAM} - * } - * @endcode + *

Reference

+ * The original paper for the P1 nonconforming element by Park and Sheen + * is accessible at https://doi.org/10.1137/S0036142902404923 , + * see @cite park2003p . * * @author Jaeryun Yim, 2015, 2016. */ diff --git a/include/deal.II/fe/mapping_cartesian.h b/include/deal.II/fe/mapping_cartesian.h index 2e507b3ac8..6a51c77cc9 100644 --- a/include/deal.II/fe/mapping_cartesian.h +++ b/include/deal.II/fe/mapping_cartesian.h @@ -31,22 +31,38 @@ DEAL_II_NAMESPACE_OPEN /** * A class providing a mapping from the reference cell to cells that are - * axiparallel. + * axiparallel, i.e., that have the shape of rectangles (in 2d) or + * boxes (in 3d) with edges parallel to the coordinate directions. The + * class therefore provides functionality that is equivalent to what, + * for example, MappingQ would provide for such cells. However, knowledge + * of the shape of cells allows this class to be substantially more + * efficient. * - * This class maps the unit cell to a grid cell with surfaces parallel to the - * coordinate lines/planes. It is specifically developed for Cartesian meshes. - * In other words, the mapping is meant for cells for which the mapping from + * Specifically, the mapping is meant for cells for which the mapping from * the reference to the real cell is a scaling along the coordinate * directions: The transformation from reference coordinates $\hat {\mathbf * x}$ to real coordinates $\mathbf x$ on each cell is of the form * @f{align*}{ - * {\mathbf x}(\hat {\mathbf x}) = \begin{pmatrix} h_x & 0 \\ 0 & h_y - * \end{pmatrix} \hat{\mathbf x} + {\mathbf v}_0 + * {\mathbf x}(\hat {\mathbf x}) + * = + * \begin{pmatrix} + * h_x & 0 \\ + * 0 & h_y + * \end{pmatrix} + * \hat{\mathbf x} + * + {\mathbf v}_0 * @f} * in 2d, and * @f{align*}{ - * {\mathbf x}(\hat {\mathbf x}) = \begin{pmatrix} h_x & 0 & 0 \\ 0 & h_y & 0 - * \\ 0 & 0 & h_z \end{pmatrix} \hat{\mathbf x} + {\mathbf v}_0 + * {\mathbf x}(\hat {\mathbf x}) + * = + * \begin{pmatrix} + * h_x & 0 & 0 \\ + * 0 & h_y & 0 \\ + * 0 & 0 & h_z + * \end{pmatrix} + * \hat{\mathbf x} + * + {\mathbf v}_0 * @f} * in 3d, where ${\mathbf v}_0$ is the bottom left vertex and $h_x,h_y,h_z$ * are the extents of the cell along the axes. -- 2.39.5