Contemporary mathematics - American Mathematical Society· 2020Q3
Finite element methods for Maxwell’s equations
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- 2020year
Short summary
Discontinuous Galerkin (DG) methods offer potential advantages over conforming edge finite element methods for approximating time-harmonic Maxwell equations, particularly for problems with spatially varying coefficients.
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Key points
- Finite element methods are surveyed for time-harmonic Maxwell equations.
- Comparison focuses on error estimates for spatially varying coefficients.
- Conforming edge methods allow piecewise smooth coefficients.
- DG methods offer potential advantages but have less advanced error analysis.
- Three DG families are considered: Interior Penalty, Hybridizable DG, and Trefftz.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Contemporary mathematics - American Mathematical Society, 2020 · DOI ↗
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Field: Computational Mechanics
Computational MechanicsEngineering