View article

In this talk we propose a mixed finite element method for solving elliptic multiscale problems. The method does neither rely on structural assumptions for the multiscale variations (such as scale separation) nor does it rely on the regularity of the solutions. The method is based on a localized orthogonal decomposition (LOD) of Raviart-Thomas finite element spaces [1]. The original concept was introduced in [4]. The approach requires to solve local problems in small patches. These computations can be perfectly parallelized and are cheap to perform. Using these local results, we construct a low dimensional" generalized" mixed finite element space for solving the original saddle point problem in an efficient way. The method is supported by a rigorous numerical analysis and various numerical experiments. Similar results were established for Lagrange elements [2, 3].