Finite Element Methods for Maxwell's Equations

2019/10/22 by Peter Monk, Monk, Peter, Yangwen Zhang +1
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1910.10069

Abstract

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.

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