From: Wolfgang Bangerth Date: Fri, 25 May 2018 11:12:32 +0000 (+0800) Subject: Add figures to the discussion in step-6. X-Git-Tag: v9.1.0-rc1~1100^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=refs%2Fpull%2F6668%2Fhead;p=dealii.git Add figures to the discussion in step-6. --- diff --git a/doc/doxygen/images/hanging_nodes_shape_functions_1.png b/doc/doxygen/images/hanging_nodes_shape_functions_1.png new file mode 100644 index 0000000000..ea36979b1c Binary files /dev/null and b/doc/doxygen/images/hanging_nodes_shape_functions_1.png differ diff --git a/doc/doxygen/images/hanging_nodes_shape_functions_2.png b/doc/doxygen/images/hanging_nodes_shape_functions_2.png new file mode 100644 index 0000000000..0a61c46799 Binary files /dev/null and b/doc/doxygen/images/hanging_nodes_shape_functions_2.png differ diff --git a/doc/doxygen/images/hanging_nodes_shape_functions_3.png b/doc/doxygen/images/hanging_nodes_shape_functions_3.png new file mode 100644 index 0000000000..e73b762fef Binary files /dev/null and b/doc/doxygen/images/hanging_nodes_shape_functions_3.png differ diff --git a/examples/step-6/doc/intro.dox b/examples/step-6/doc/intro.dox index 6d375e5d31..8c8004c3e2 100644 --- a/examples/step-6/doc/intro.dox +++ b/examples/step-6/doc/intro.dox @@ -123,7 +123,29 @@ cannot be bilinear because then it needs to be linear along each edge of the large cell, and that means that it needs to be zero on the entire edge because it needs to be zero on the two vertices of the large cell on that edge. But it is not zero at the hanging node itself -when seen from the small cells' side -- so it is not continuous. +when seen from the small cells' side -- so it is not continuous. The +following three figures show three of the shape functions along the +edges in question that turn out to not be continuous when defined in +the usual way simply based on the cells they are adjacent to: + +
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+ @image html hanging_nodes_shape_functions_1.png "A discontinuous shape function adjacent to a hanging node" +
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+ @image html hanging_nodes_shape_functions_2.png "A discontinuous shape function at a hanging node" +
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+ @image html hanging_nodes_shape_functions_3.png "A discontinuous shape function adjacent to a hanging node" +
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+ But we do want the finite element solution to be continuous so that we have a “conforming finite element method” where the