## Preprint 2010-25

## Tomás Barrios, Rommel Bustinza:

### An augmented discontinuous Galerkin method for stationary Stokes problem

### Abstract:

In this paper we present an augmented mixed discontinuous formulation for the stationary Stokes problem. More precisely, we derive a new stabilized discontinuous formulation by adding appropriate Galerkin least squares terms to the velocity-pseudostress formulation associated to Stokes problem. Then, using the Lax-Milgram theorem, we prove the well-posedness of the resulting discrete scheme, and under suitable regularity assumptions, we obtain the optimal rate of convergence of the method, with respect to the h-version. Finally, several numerical experiments confirming the theoretical properties of the augmented discontinuous scheme are also reported.

This preprint gave rise to the following definitive publication(s):

**Tomás BARRIOS, Rommel BUSTINZA: ***An a posteriori error analysis of an augmented discontinuous Galerkin formulation for Darcy flow*. Numerische Mathematik, vol. 120, 2, pp. 231-269, (2012).