Finite Element Methods for Maxwell's Equations
Finite Element Methods for Maxwell's Equations
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DOI：
10.1090/conm/754/15143
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发表时间：
2019-10
期刊：
影响因子：
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通讯作者：
P. Monk;Yangwen Zhang
中科院分区：
文献类型：
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作者：
P. Monk;Yangwen Zhang
本文综述了时间谐波麦克斯韦方程的有限元近似方法。我们专注于比较空间变化系数的问题的误差估计。对于协调边有限元方法，这样的估计允许，至少，分段光滑的系数。但是对于不连续Galerkin（DG）方法，误差分析的最新技术还不太先进（我们考虑了三种DG方法族：内部惩罚型，Hybridizable DG和Trefftz型方法）。然而，DG方法提供了显着的潜在优势相比，符合的方法。
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.