The mortar finite element method for 3D Maxwell equations: First results

In the framework of domain decomposition methods, we extend the main ideas of the mortar element method to the numerical solution of Maxwell's equatio ns (in wave form) by H (curl)-conforming finite elements. The method we pro pose turns out to be a new nonconforming, nonoverlapping domain decompositi on method where nonmatching grids are allowed at the interfaces between sub domains. A model problem is considered, the convergence of the discrete app roximation is analyzed, and an error estimate is provided. The method is pr oven to be slightly suboptimal with a loss of a factor root |1nh| with resp ect to the degree of polynomials. In order to achieve this convergence resu lt we nevertheless need extra-regularity assumptions on the solution of the continuous problem.