Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2007; 44(5): 1103-1119

Printed September 1, 2007

Copyright © The Korean Mathematical Society.

A multiscale mortar mixed finite element method for slightly compressible flows in porous media

Mi-Young Kim, Eun-Jae Park, Sunil G. Thomas, and Mary F. Wheeler

Inha University, Yonsei University, The University of Texas at Austin

Abstract

We consider multiscale mortar mixed finite element discretizations for slightly compressible Darcy flows in porous media. This paper is an extension of the formulation introduced by Arbogast et al. for the incompressible problem [2]. In this method, flux continuity is imposed via a mortar finite element space on a coarse grid scale, while the equations in the coarse elements (or subdomains) are discretized on a fine grid scale. Optimal fine scale convergence is obtained by an appropriate choice of mortar grid and polynomial degree of approximation. Parallel numerical simulations on some multiscale benchmark problems are given to show the efficiency and effectiveness of the method.

Keywords: multiscale, mixed finite element, mortar finite element, error estimates, multiblock, non-matching grids

MSC numbers: 65M15, 65M60, 76A05, 76M10,76S05