Axel Målqvist
Division of Scientific Computing
Department of Information Technology
Uppsala University
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 promising results.