A Penalty-Free Asymmetric Nitsche's Method for Edge Elements
Provides a theoretical stability guarantee for a numerical method that simplifies boundary condition enforcement in computational electromagnetics, though the result is incremental as it extends existing Nitsche techniques to edge elements.
The paper proves inf-sup stability of a penalty-free asymmetric Nitsche's method for Nédélec edge elements on tetrahedral meshes under an isolated patch condition, enabling weak imposition of tangential Dirichlet boundary conditions for curl-curl problems.
We show the stability of a penalty-free asymmetric Nitsche's method using Nédélec 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.