arXiv

Geometric decompositions of the simplicial lattice and smooth finite elements in arbitrary dimension

Long Chen and Xuehai Huang

arXiv

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ABSTRACT:

Recently Cm-conforming finite elements on simplexes in
arbitrary dimension are constructed by Hu, Lin and Wu. The key in the
construction is a non-overlapping decomposition of the simplicial
lattice in which each component will be used to determine the normal
derivatives at each lower dimensional sub-simplex. A geometric
approach is proposed in this paper and a geometric decomposition of
the finite element spaces is given. Our geometric decomposition using
the graph distance not only simplifies the construction but also
provides an easy way of implementation.