Finite Element Methods for Maxwell's Equations
Peter Monk
- 19 Jun 2003
320
TL;DR: Finite element methods for Maxwell's equations with spatially varying coefficients are surveyed. Error estimates are reviewed for conforming and DG methods. DG methods offer potential advantages over conforming methods despite less advanced error analysis.
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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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References
Finite elements in computational electromagnetism
TL;DR: In this paper, finite element Galerkin schemes for a number of linear model problems in electromagnetism were discussed, and the finite element schemes were introduced as discrete differential forms, matching the coordinate-independent statement of Maxwell's equations in the calculus of differential forms.
Weighted regularization of Maxwell equations in polyhedral domains
Martin Costabel,Monique Dauge +1 more
TL;DR: A new method of regularizing time harmonic Maxwell equations by a {\bf grad}-div term adapted to the geometry of the domain is presented, which proves to be numerically efficient.
On traces for functional spaces related to Maxwell's equations Part I: An integration by parts formula in Lipschitz polyhedra
Annalisa Buffa,Patrick Ciarlet +1 more
TL;DR: In this paper, the tangential trace and tangential components of fields which belong to the space H(curl, Omega), when Omega is a polyhedron with Lipschitz continuous boundary are studied.
Fortin operator and discrete compactness for edge elements
TL;DR: The aim of the present paper is to show how to construct a Fortin operator which converges uniformly to the identity in the spirit of [5,4], and to apply this result to the analysis of the approximation of the time-harmonic Maxwell's system.