Finite element spaces by Whitney k-forms on cubical meshes

TL;DR

This paper introduces finite element spaces using Whitney k-forms on cubical meshes, enabling compatible discretizations for HΛ^k problems and constructing discrete de Rham complexes.

Contribution

It presents a novel approach to finite element spaces on cubical meshes with Whitney k-forms, including compatible discretizations and discrete de Rham complexes.

Findings

Constructed finite element spaces by Whitney k-forms on cubical meshes.

Developed compatible discretizations for HΛ^k problems.

Built discrete de Rham complexes and commutative diagrams.

Abstract

Finite element spaces by Whitney $k$-forms on cubical meshes in $\mathbb{R}^n$ are presented. Based on the spaces, compatible discretizations to $H\Lambda^k$ problems are provided, and discrete de Rham complexes and commutative diagrams are constructed.