Simple finite element schemes for the solution of the curl-div system

TL;DR

This paper introduces new variational formulations and finite element schemes for solving the curl-div system, demonstrating convergence using curl-free and divergence-free finite elements.

Contribution

It proposes novel variational formulations and finite element methods specifically designed for the curl-div system, with proven convergence properties.

Findings

Finite element approximations converge for the curl-div system.

Use of curl-free and divergence-free finite elements improves discretization.

New formulations enhance numerical solution accuracy.

Abstract

New variational formulations are devised for the curl--div system, and the corresponding finite element approximations are shown to converge. Curl--free and divergence--free finite elements are employed for discretizing the problem.