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Finite element methods with matching and nonmatching meshes for Maxwell equations with discontinuous coefficients. (English) Zbl 0964.78017
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.
MSC:
 78M10 Finite element methods (optics) 78A25 General electromagnetic theory 35Q60 PDEs in connection with optics and electromagnetic theory 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems