From 2f565578044e5b95bafed8f8c14d9dc966c3d2d3 Mon Sep 17 00:00:00 2001 From: wolf Date: Fri, 11 Dec 1998 10:24:40 +0000 Subject: [PATCH] Doc update. git-svn-id: https://svn.dealii.org/trunk@701 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/deal.II/include/fe/fe.h | 40 ++++++++++++++++++++++++++++++++- 1 file changed, 39 insertions(+), 1 deletion(-) diff --git a/deal.II/deal.II/include/fe/fe.h b/deal.II/deal.II/include/fe/fe.h index 836f4c892a..144d29b2ec 100644 --- a/deal.II/deal.II/include/fe/fe.h +++ b/deal.II/deal.II/include/fe/fe.h @@ -309,7 +309,10 @@ struct FiniteElementBase : * to the destination cell, i.e. the * unrefined one, while the column indices * are for the refined cell's degrees of - * freedom. + * freedom. The application of this matrix + * is therefore usually its being + * multiplied by the vector of nodal values + * on the child. * * In essence, using the matrices from the * children to the mother cell amounts to @@ -329,6 +332,41 @@ struct FiniteElementBase : * contributions of each child into the * nodal value vector of the mother cell. * + * While we could avoid this and rather add + * up the contributions of each child for + * nodes that are interior of the mother + * cell, we can't for nodes on the boundary + * of the mother cell. The reason for this + * is that we know how many children may + * contribute to the interpolated nodal + * value of an interior degree of freedom. + * However, we don't know for dofs on the + * boundary, for which we only know how many + * children from each side of the face + * contribute, but we would have to look out + * of the cell to know how many neighbors + * there are and then, still, we would have + * to have two different interpolation + * routines for local interpolation and for + * the contribution of a cell to a global + * interpolation if we wanted to compute + * that by adding up local contributions. + * + * Because of this problem, we chose to + * write rather than add the contributions + * of each cell to the interpolation onto + * the mother cell. However, there now is + * another problem which appears when using + * discontinuous finite elements. The + * process of 'writing' assumed that we + * get the same result for each degree of + * freedom from each of the children, such + * that 'over'writing would not destroy + * information; when using discontinuous + * elements, this assumption is violated. + * + * SOLUTION? NOT YET MADE UP! + * * To compute the interpolation of a * finite element field to a cell, you * may use the #get_interpolated_dof_values# -- 2.39.5