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

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 finite number of subdomains. Further, an error analysis for the finite element approximation of the penalty formulation is given. Finally, numerical experiments on a series of model second order problems are presented.