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. 1

Auxiliary Space Preconditioning of Finite Element Equations Using a Nonconforming Interior Penalty Reformulation and Static Condensation

We modify the well-known interior penalty finite element discretization method so that it allows for element-by-element assembly. This is possible due to the introduction of additional unknowns associated with the interfaces between neighboring elements. The resulting bilinear form, and a Schur complement (reduced) version of it, are utilized in a number of auxiliary space preconditioners for the original conforming finite element discretization problem. These preconditioners are analyzed on the fine scale and their performance is illustrated on model second order scalar elliptic problems discretized with high order elements