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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