A Penalty-Free Asymmetric Nitsche's Method for Edge Elements

TL;DR

This paper introduces a stable, penalty-free asymmetric Nitsche's method using Nédélec edge elements for curl-curl problems, with proven inf-sup stability under mesh conditions, applicable to electromagnetic and magnetic problems.

Contribution

It demonstrates the stability of a novel penalty-free asymmetric Nitsche's method for edge elements, expanding the toolkit for curl-curl problem discretizations.

Findings

Proves inf-sup stability under mesh conditions

Applicable to curl-elliptic and magnetic advection-diffusion problems

Eliminates penalty parameters in Nitsche's method

Abstract

We show the stability of a penalty-free asymmetric Nitsche's method using N\'ed\'elec edge elements for solving curl-curl-type problems with tangential Dirichlet boundary conditions imposed weakly. The main result is an inf-sup stability estimate for the asymmetric bilinear form under an isolated patch condition on the tetrahedral mesh. Applications to a curl-elliptic problem and a magnetic advection-diffusion problem are discussed.