Almost optimal interior penalty discontinuous approximations of symmetric elliptic problems on non-matching grids

Abstract. We consider an interior penalty discontinuous approximation for sym-metric 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 approxi-mation of the original problem based on the partition of the domain into a finite number of subdomains. Further, an error analysis for the finite element approxi-mation of the penalty formulation is given. Finally, numerical experiments on a series of model second order problems are presented. 1