From 8f0f911bbc334387c82e2831af6a8db3c095bc3e Mon Sep 17 00:00:00 2001 From: brian Date: Tue, 17 Dec 2002 17:06:53 +0000 Subject: [PATCH] rewrote documentation. git-svn-id: https://svn.dealii.org/trunk@6844 0785d39b-7218-0410-832d-ea1e28bc413d --- .../deal.II/include/fe/fe_q_hierarchical.h | 53 ++++++++----------- 1 file changed, 22 insertions(+), 31 deletions(-) diff --git a/deal.II/deal.II/include/fe/fe_q_hierarchical.h b/deal.II/deal.II/include/fe/fe_q_hierarchical.h index c3cdbe7a8a..949d04c42f 100644 --- a/deal.II/deal.II/include/fe/fe_q_hierarchical.h +++ b/deal.II/deal.II/include/fe/fe_q_hierarchical.h @@ -28,10 +28,27 @@ template class MappingQ; * Implementation of Hierarchical finite elements @p{Qp} that yield the * finite element space of continuous, piecewise polynomials of degree * @p{p}. This class is realized using tensor product polynomials - * based on a hierarchical basis of the interval @p{[-1,1]} suitable - * for building an @p{hp} tensor product finite element. There are not - * many differences between @p{FE_Q_Hierarchical} and @p{FE_Q}, except - * that we now allow the degree to be nonconstant for @p{p}-refinement. + * based on a hierarchical basis @p{Hierarchical} of the interval + * @p{[0,1]} which is suitable for building an @p{hp} tensor product + * finite element, if we assume that each element has a single degree. + * + * There are not many differences between @p{FE_Q_Hierarchical} and + * @p{FE_Q}, except that we add a function @p{embedding_dofs} that takes + * a given integer @p{q}, between @p{1} and @p{p}, and + * returns the numbering of basis functions of the element of order + * @p{q} in basis of order @p{p}. This function is + * useful if one wants to make calculations using the hierarchical + * nature of these shape functions. + * + * The unit support points now are reduced to @p{0}, @p{1}, and @p{0.5} in + * one dimension, and tensor products in higher dimensions. Thus, various + * interpolation functions will only work correctly for the linear case. + * Future work will involve writing projection--interpolation operators + * that can interpolate onto the higher order bubble functions. + * + * The various constraint, prolongation, and restriction matrices are + * now available in all dimensions for all degrees @p{p}, currently up to + * order 19. * * The constructor of this class takes the degree @p{p} of this finite * element. @@ -43,32 +60,6 @@ template class MappingQ; * polynomials of degree @p{p}. This @p{TensorProductPolynomials} * object provides all values and derivatives of the shape functions. * - * Furthermore the constructor filles the @p{interface_constraints}, - * the @p{prolongation} (embedding) and the @p{restriction} - * matrices. These are implemented only up to a certain degree, that - * is listed in the following: (fix this eventually......) - * - * @begin{itemize} - * @item @p{dim==1} - * @begin{itemize} - * @item the @p{interface_constraints} are not needed - * @item the @p{prolongation} matrices up to degree 4, and - * @item the @p{restriction} matrices up to degree 4. - * @end{itemize} - * @item @p{dim==2} - * @begin{itemize} - * @item the @p{interface_constraints} up to degree 4, - * @item the @p{prolongation} matrices up to degree 3, and - * @item the @p{restriction} matrices up to degree 4. - * @end{itemize} - * @item @p{dim==3} - * @begin{itemize} - * @item the @p{interface_constraints} up to degree 2, - * @item the @p{prolongation} matrices up to degree 2, and - * @item the @p{restriction} matrices up to degree 4. - * @end{itemize} - * @end{itemize} - * * @sect3{Numbering of the degrees of freedom (DoFs)} * * The original ordering of the shape functions represented by the @@ -77,7 +68,7 @@ template class MappingQ; * beginning with the shape functions whose support points are at the * vertices, then on the line, on the quads, and finally (for 3d) on * the hexes. To be explicit, these numberings are listed in the - * following: (support points for @p{hp}??) + * following: * * @sect4{Q1 elements} * @begin{itemize} -- 2.39.5