Finite Element Methods for Maxwell's Equations

By Peter B. Monk, Yangwen Zhang. 75 Years of Mathematics of Computation, 2019

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We survey finite element methods for approximating the time harmonic Maxwell equations. We concentrate on comparing error estimates for problems with spatially varying coefficients. For the conforming edge finite element methods, such estimates allow, at least, piecewise smooth coefficients. But for Discontinuous Galerkin (DG) methods, the state of the art of error analysis is less advanced (we consider three DG families of methods: Interior Penalty type, Hybridizable DG, and Trefftz type methods). Nevertheless, DG methods offer significant potential advantages compared to conforming methods.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/5bad7686ece8a82c486148534bb01075c01d7b76