From a958c98e5fbe261468121423bd02f0512940e47e Mon Sep 17 00:00:00 2001 From: JaeryunYim Date: Thu, 4 Aug 2016 20:08:17 +0900 Subject: [PATCH] Add. --- include/deal.II/fe/fe_p1nc.h | 19 +++++++++++++++---- 1 file changed, 15 insertions(+), 4 deletions(-) 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. -- 2.39.5