A primal finite element scheme of the $\mathbf{H}(\mathbf{d})\cap \mathbf{H}(\boldsymbol{\delta})$ elliptic problem

TL;DR

This paper introduces a unified finite element scheme for solving a class of elliptic problems involving differential forms in multiple dimensions, enhancing computational methods for complex PDEs.

Contribution

It presents a new family of finite element schemes for the primal weak formulation of high-dimensional $H( extbf{d}) igcap H(oldsymbol{ abla})$ elliptic problems, applicable for various dimensions and orders.

Findings

Unified finite element schemes for $H( extbf{d}) igcap H(oldsymbol{ abla})$ problems

Applicable for dimensions $n geq 2$ and orders $1 leq k leq n-1$

Provides a framework for numerical solutions of complex elliptic PDEs.

Abstract

In this paper, a unified family, for $n\geqslant2$ and $1\leqslant k \leqslant n-1$, of finite element schemes are presented for the primal weak formulation of the $n$-dimensional $H(\mathbf{d}^k)\cap H(\boldsymbol{\delta}_k)$ elliptic problem.