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Zbl 0964.78017
Chen, Zhiming; Du, Qiang; Zou, Jun
Finite element methods with matching and nonmatching meshes for Maxwell equations with discontinuous coefficients.
(English)
[J] SIAM J. Numer. Anal. 37, No.5, 1542-1570 (2000). ISSN 0036-1429; ISSN 1095-7170/e

The authors consider finite element methods for the solution of Maxwell's equations in piecewise continuous media. They develop error estimates, and discuss both matching and non-matching meshes on the interface between the media. A variational formulation is given. During the course of the analysis a Lagrangian multiplier is introduced in association with the charge divergence equation $\nabla.D= \rho$. The tone of the paper is extremely abstract, much use being made of abstract spaces and there is no actual problem solved as an illustration of the methods discussed.
[Ll.G.Chambers (Bangor)]
MSC 2000:
*78M10 Finite element methods (optics)
78A25 General electromagnetic theory
35Q60 PDE of electromagnetic theory and optics
46E35 Sobolev spaces and generalizations

Keywords: finite element method; Maxwell equations; interface problems; nonmatching meshes; error estimates; saddle point formulation; extension theorem; finite element methods; Maxwell's equations; piecewise continuous media; matching; non-matching meshes; variational formulation; Lagrangian multiplier; charge divergence equation

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