Convergence of Lagrange Finite Element Methods for Maxwell Eigenvalue Problem in 3D

preprint2022arXivOpen access

Abstract

We prove convergence of the Maxwell eigenvalue problem using quadratic or higher Lagrange finite elements on Worsey-Farin splits in three dimensions. To do this, we construct two Fortin-like operators to prove uniform convergence of the corresponding source problem. We present numerical experiments to illustrate the theoretical results.

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