Online mixed multiscale finite element method with oversampling and its applications
For computational geoscience, this provides an incremental improvement to multiscale methods for flow in heterogeneous media.
The paper extends online mixed generalized multiscale methods by computing online basis functions via Neumann problems in over-sampled domains, demonstrating improved accuracy for flow problems in highly heterogeneous porous media through numerical experiments.
In this paper, we consider an online basis enrichment mixed generalized multiscale method with oversampling, for solving flow problems in highly heterogeneous porous media. This is an exten- sion of the online mixed generalized multiscale method [6]. The multiscale online basis functions are computed by solving a Neumann problem in an over-sampled domain, instead of a standard neighborhood of a coarse face. We are motivated by the restricted domain decomposition method. Extensive numerical experiments are presented to demonstrate the performance of our methods for both steady-state flow, and two-phase flow and transport problems.