Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published June 28, 2002 | Published
Journal Article Open

A mixed multiscale finite element method for elliptic problems with oscillating coefficients

Abstract

The recently introduced multiscale finite element method for solving elliptic equations with oscillating coefficients is designed to capture the large-scale structure of the solutions without resolving all the fine-scale structures. Motivated by the numerical simulation of flow transport in highly heterogeneous porous media, we propose a mixed multiscale finite element method with an over-sampling technique for solving second order elliptic equations with rapidly oscillating coefficients. The multiscale finite element bases are constructed by locally solving Neumann boundary value problems. We provide a detailed convergence analysis of the method under the assumption that the oscillating coefficients are locally periodic. While such a simplifying assumption is not required by our method, it allows us to use homogenization theory to obtain the asymptotic structure of the solutions. Numerical experiments are carried out for flow transport in a porous medium with a random log-normal relative permeability to demonstrate the efficiency and accuracy of the proposed method.

Additional Information

© 2002 American Mathematical Society. Received by editor(s): March 21, 2000; received by editor(s) in revised form: July 10, 2000 and May 29, 2001. We wish to thank Dr. Yalchin R. Efendiev for many inspiring discussions and for providing us the code generating the log-normal permeability field. We would also like to thank Dr. Hector Ceniceros for his valuable comments on our original manuscript, and the referee for his careful reading and constructive comments. The first author was supported in part by China NSF under the grants 19771080 and 10025102 and by China MOS under the grant G1999032804. The second author was supported in part by NSF under the grant DMS-0073916 and by ARO under the grant DAAD19-99-1-0141.

Attached Files

Published - CHEmc03.pdf

Files

CHEmc03.pdf
Files (2.0 MB)
Name Size Download all
md5:308d2126e91636fe4d9847252dcc812a
2.0 MB Preview Download

Additional details

Created:
August 21, 2023
Modified:
October 16, 2023