]> https://gitweb.dealii.org/ - dealii-svn.git/commitdiff
Add two more notes to the documentation of that function.
authorwolf <wolf@0785d39b-7218-0410-832d-ea1e28bc413d>
Tue, 28 Jun 2005 16:18:26 +0000 (16:18 +0000)
committerwolf <wolf@0785d39b-7218-0410-832d-ea1e28bc413d>
Tue, 28 Jun 2005 16:18:26 +0000 (16:18 +0000)
git-svn-id: https://svn.dealii.org/trunk@10956 0785d39b-7218-0410-832d-ea1e28bc413d

deal.II/deal.II/include/fe/fe_tools.h

index b13b3ae2a6cc09391cfdf1a6e7a6fea8c7ed675a..d504f7fdd96ae8a2a0069d78170d4af81e3b4cfc 100644 (file)
@@ -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
+                                     * <tt>ths_quadrature</tt> equal
+                                     * <tt>fe.get_unit_support_points()</tt>,
+                                     * 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 <tt>Q</tt> in
+                                     * that case is the identity
+                                     * matrix, the mass matrix
+                                     * <tt>M</tt> is not equal to the
+                                     * identity matrix, except for
+                                     * the special case that the
+                                     * quadrature formula
+                                     * <tt>lhs_quadrature</tt> also
+                                     * has its quadrature points in
+                                     * the support points of the
+                                     * finite element.
                                       */
     template <int dim>
     static

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