Adaptive finite element method for the Maxwell eigenvalue problem

TL;DR

This paper proves the optimal convergence of an adaptive finite element method using edge elements for solving Maxwell's eigenvalue problem, ensuring accurate electromagnetic simulations.

Contribution

It establishes the first proof of optimal convergence for an adaptive scheme applied to Maxwell eigenvalue problems using edge finite elements.

Findings

Proves optimal convergence of the adaptive scheme.

Uses equivalence with a mixed eigenvalue problem for the proof.

Enhances reliability of electromagnetic eigenvalue computations.

Abstract

In this paper we prove the optimal convergence of a standard adaptive scheme based on edge finite elements for the approximation of the solutions of the eigenvalue problem associated with Maxwell's equations. The proof uses the known equivalence of the problem of interest with a mixed eigenvalue problem.