# Malqvist 200710

### From NA-Wiki

**Speaker:** Axel MÃ¥lqvist, Uppsala University

**Title:** Adaptive variational multiscale methods

**When:** The NA seminar meets on Oct 17 at 15:15 in D4523

**Abstract**

We present an adaptive multiscale method for solving elliptic partial differential equations. The method is based on numerical solution of decoupled local fine scale problems on patches. Critical parameters such as fine and coarse scale mesh size and patch size are tuned automatically by an adaptive algorithm based on a posteriori error estimates. We extend the method to a mixed formulation of the Poisson equation and to a convection dominated convection-diffusion problem. In both cases we derive error estimates and present adaptive algorithms. We apply the method mixed to an elliptic problem that arises in oil reservoir simulation and show promissing results.