From: JaeryunYim Date: Thu, 4 Aug 2016 11:08:17 +0000 (+0900) Subject: Add. X-Git-Tag: v8.5.0-rc1~624^2~25 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=a958c98e5fbe261468121423bd02f0512940e47e;p=dealii.git Add. --- diff --git a/include/deal.II/fe/fe_p1nc.h b/include/deal.II/fe/fe_p1nc.h index b5edb00590..44bb59ed7b 100644 --- a/include/deal.II/fe/fe_p1nc.h +++ b/include/deal.II/fe/fe_p1nc.h @@ -53,14 +53,18 @@ DEAL_II_NAMESPACE_OPEN * It means that the genuine number of independent dofs on a quad is 3, * and it is the same number to the dimension of the linear polynomial space in 2D. * - * The canonical basis functions are given as any three shape functions of + + * For each vertex v_j, there are two edges of which v_j is one of the end points. + * Consider the linear function such that one half at two midpoints of such edges, + * and zero at two midpoints of other edges. + * Note that this situation satisfies the dice rule which is described above. + * We denote such a function by \phi_j. + + * The canonical (local) basis functions are given as any three shape functions of * the following four linear functions: * * \phi_1, \phi_2, \phi_3, \phi_4. * - * for each vertex v_j, there are two edges of which v_j is one of the end points. - * Consider the linear function such that one half at two midpoints of such edges, - * and zero at two midpoints of other edges. * 2 -------|------- 3 @@ -76,6 +80,13 @@ DEAL_II_NAMESPACE_OPEN * 0 -------|------- 1 + + * The (global) basis function associated with a node is defined by the composition of + * (local) basis functions associated with the node on each element. + * In case of the problem with homogeneous Dirichlet boundary condition, + * the number of DOFs is equal to the number of interior nodes. + + * You can find the paper about the P1NC element at * http://epubs.siam.org/doi/abs/10.1137/S0036142902404923.