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

Understand

Recently $C^m$-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.