Online mixed multiscale finite element method with oversampling and its applications

TL;DR

This paper introduces an online mixed multiscale finite element method with oversampling for flow problems in heterogeneous media, enhancing accuracy through basis enrichment and demonstrating effectiveness in various flow simulations.

Contribution

The paper extends existing online multiscale methods by incorporating oversampling and restricted domain decomposition, improving solution accuracy and computational efficiency.

Findings

Effective in steady-state flow simulations

Applicable to two-phase flow and transport problems

Demonstrates improved accuracy with oversampling

Abstract

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.