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

11/21/2021
by   Long Chen, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/29/2021

Geometric Decompositions of Div-Conforming Finite Element Tensors

A unified construction of div-conforming finite element tensors, includi...
research
06/02/2022

Finite Element Complexes in Two Dimensions

Two-dimensional finite element complexes with various smoothness, includ...
research
05/23/2022

Entanglements

Robertson and Seymour constructed for every graph G a tree-decomposition...
research
02/05/2023

Discrete tensor product BGG sequences: splines and finite elements

In this paper, we provide a systematic discretization of the Bern­stein-...
research
09/15/2021

On Characterization of Finite Geometric Distributive Lattices

A Lattice is a partially ordered set where both least upper bound and gr...
research
06/25/2021

Finite elements for divdiv-conforming symmetric tensors in arbitrary dimension

Several div-conforming and divdiv-conforming finite elements for symmetr...
research
12/03/2021

Unifying the geometric decompositions of full and trimmed polynomial spaces in finite element exterior calculus

Arnold, Falk, Winther, in _Finite element exterior calculus, homolog...

Please sign up or login with your details

Forgot password? Click here to reset