A Tensor-Product Finite Element Cochain Complex with Arbitrary Continuity
Numerical Analysis
2023-10-25 v1 Numerical Analysis
Abstract
We develop tensor product finite element cochain complexes of arbitrary smoothness on Cartesian meshes of arbitrary dimension. The first step is the construction of a one-dimensional -conforming finite element cochain complex based on a modified Hermite interpolation operator, which is proved to commute with the exterior derivative by means of a general commutation lemma. Adhering to a strict tensor product construction we then derive finite element complexes in higher dimensions.
Cite
@article{arxiv.2207.00309,
title = {A Tensor-Product Finite Element Cochain Complex with Arbitrary Continuity},
author = {Francesca Bonizzoni and Guido Kanschat},
journal= {arXiv preprint arXiv:2207.00309},
year = {2023}
}