Expanded Mixed Multiscale Finite Element Methods and Their Applications for Flows in Porous Media

Jiang, L.; Copeland, D.; Moulton, J. D.

Expanded Mixed Multiscale Finite Element Methods and Their Applications for Flows in Porous Media

Type

Article

Authors

Jiang, L.
Copeland, D.
Moulton, J. D.

KAUST Grant Number

KUS-C1-016-04

Date

2012-01

Abstract

We develop a family of expanded mixed multiscale finite element methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed multiscale finite element formulation in the sense that four unknowns (hybrid formulation) are solved simultaneously: pressure, gradient of pressure, velocity, and Lagrange multipliers. We use multiscale basis functions for both the velocity and the gradient of pressure. In the expanded mixed MsFEM framework, we consider both separable and nonseparable spatial scales. Specifically, we analyze the methods in three categories: periodic separable scales, G-convergent separable scales, and a continuum of scales. When there is no scale separation, using some global information can significantly improve the accuracy of the expanded mixed MsFEMs. We present a rigorous convergence analysis of these methods that includes both conforming and nonconforming formulations. Numerical results are presented for various multiscale models of flow in porous media with shale barriers that illustrate the efficacy of the proposed family of expanded mixed MsFEMs. © 2012 Society for Industrial and Applied Mathematics.

Citation

Jiang L, Copeland D, Moulton JD (2012) Expanded Mixed Multiscale Finite Element Methods and Their Applications for Flows in Porous Media. Multiscale Model Simul 10: 418–450. Available: http://dx.doi.org/10.1137/11083143X.

Acknowledgements

This author's research was supported by the Department of Energy at Los Alamos National Laboratory under contract DE-AC52-06NA25396 and the DOE Office of Science Advanced Computing Research (ASCR) program in Applied Mathematical Sciences.This author's research was supported by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).