MULTISCALE METHODS FOR ELLIPTIC PROBLEMS

In this paper we derive a framework for multiscale approximation of elliptic problems on standard and mixed form. The method presented is based on a splitting into coarse and fine scales together with a systematic technique for approximation of the fine scale part, based on the solution of decoupled localized subgrid problems. The fine scale approximation is then used to modify the coarse scale equations. A key feature of the method is that symmetry in the bilinear form is preserved in the discrete system. Other key features are a posteriori error bounds and adaptive algorithms based on these bounds. The adaptive algorithms are used for automatic tuning of the method parameters. In the last part of the paper we present numerical examples where we apply the framework to a problem in oil reservoir simulation.