Speaker: Jiang, Lijian (IMA)
Title: Mixed multiscale finite element methods using approximate global information and their applications in heterogeneous porous media
Abstract: We propose a framework of mixed MsFEMs using approximate global information based on partial upscaling. A requirement for partial homogenization/upscaling is to capture long-range (non-local) effects present in the fine-scale solution, while homogenizing some of the smallest scales. The local information at these smallest scales is captured in the computation of basis functions. Thus, the proposed approach allows us to avoid the computations at the scales that can be homogenized. This results to coarser problems for the computation of global fields. The mixed MsFEMs are able to improve accuracy significantly compared to local mixed MsFEMs. The mixeds MsFEMs can work efficiently for the problems with non-separable hierarchical scales. Analysis is given for the proposed methods. We show the applications of the mixed MsFEMs to deterministic porous media and stochastic porous media.