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ALMOST OPTIMAL INTERIOR PENALTY DISCONTINUOUS APPROXIMATIONS OF SYMMETRIC ELLIPTIC PROBLEMS ON NON MATCHING GRIDS R D LAZAROV J E PASCIAK J SCHO BERL AND P S VASSILEVSKI Abstract We consider an interior penalty discontinuous approximation for symmetric elliptic problems of second order on non matching grids in this paer The main result is an almost optimal error estimate for the interior penalty approximation of the original problem based on the partition of the domain into a nite number of subdomains Further an error analysis for the nite element approximation of the penalty formulation is given Finally numerical experiments on a series of model second order problems are presented 1 Introduction In this paper we propose and analyze a simple strategy to construct composite discretizations of self adjoint second order elliptic equations on non matching grids The need for discretizations on non matching grids is motivated partially from the desire for parallel discretization methods including adaptive for PDEs which is a much easier task if non matching grids are allowed across the subdomain boundaries Another situation may arise when di erent discretizations techniques are utilized in di erent parts of the subdomains and there is no a priori guarantee that the meshes will be aligned Our method can be described as interior penalty approximation based on partially discontinuous elements The mortar method is a general technique for handling discretizations on non matching grids However our motivation for using the penalty approach is that it eliminates the need for additional Lagrange multiplier or mortar spaces There is a vast number of publications devoted to the mortar nite element method as a general strategy for deriving discretization methods on non matching grids We refer the interested reader to the series of Proceedings of the International Conferences on Domain Decomposition Methods cf e g 5 11 17 for more information see http www ddm org In the present paper

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