From: wolf Date: Tue, 28 Jun 2005 16:18:26 +0000 (+0000) Subject: Add two more notes to the documentation of that function. X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=2c1d90df08e15a79763934c5b84f80f836b4a263;p=dealii-svn.git Add two more notes to the documentation of that function. git-svn-id: https://svn.dealii.org/trunk@10956 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/deal.II/include/fe/fe_tools.h b/deal.II/deal.II/include/fe/fe_tools.h index b13b3ae2a6..d504f7fdd9 100644 --- a/deal.II/deal.II/include/fe/fe_tools.h +++ b/deal.II/deal.II/include/fe/fe_tools.h @@ -325,6 +325,47 @@ class FETools * matter if you use a continuous * or discontinuous version of * the finite element. + * + * It is worth noting that there + * are a few confusing cases of + * this function. The first one + * is that it really only makes + * sense to project onto a finite + * element that has at most as + * many degrees of freedom per + * cell as there are quadrature + * points; the projection of N + * quadrature point data into a + * space with M>N unknowns is + * well-defined, but often yields + * funny and non-intuitive + * results. Secondly, one would + * think that if the quadrature + * point data is defined in the + * support points of the finite + * element, i.e. the quadrature + * points of + * ths_quadrature equal + * fe.get_unit_support_points(), + * then the projection should be + * the identity, i.e. each degree + * of freedom of the finite + * element equals the value of + * the given data in the support + * point of the corresponding + * shape function. However, this + * is not generally the case: + * while the matrix Q in + * that case is the identity + * matrix, the mass matrix + * M is not equal to the + * identity matrix, except for + * the special case that the + * quadrature formula + * lhs_quadrature also + * has its quadrature points in + * the support points of the + * finite element. */ template static