Istituto di Matematica Applicata e Tecnologie Informatiche     
F. Ben Belgacem A. B. Y. M. The Mortar Finite Element Method for 3D Maxwell Equations: First Results. Technical report ercim.cnr.ian//1999-1141, 1999.
In the framework of domain decomposition, we extend the main ideas of the mortar element method to the numerical resolution of Maxwell's equations (in wave form) by $H(curl)$-conforming finite elements. The method we propose turns out to be a new nonconforming nonoverlapping domain decomposition method where nonmatching grids are allowed at the interfaces between subdomains. A model problem is considered, the convergence of the discrete approximation is analyzed and an error estimate is provided. The method is proven to be slightly sub-optimal with a loose of a factor $sqrt{|ln h|}$ with respect to the degree of polynomials. In order to achieve this convergence result we nevertheless need extra-regularity assumptions on the solution of the continuous problem.
Subject 65N12, 65N30, 65N55, 78A30

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