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Journal of Numerical Mathematics

Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri

Managing Editor: Olshanskii, Maxim

Editorial Board Member: Benzi, Michele / Brenner, Susanne C. / Carstensen, Carsten / Dryja, M. / Feistauer, Miloslav / Glowinski, R. / Lazarov, Raytcho / Nataf, Frédéric / Neittaanmaki, P. / Bonito, Andrea / Quarteroni, Alfio / Guzman, Johnny / Rannacher, Rolf / Repin, Sergey I. / Shi, Zhong-ci / Tyrtyshnikov, Eugene E. / Zou, Jun / Simoncini, Valeria / Reusken, Arnold

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Online
ISSN
1569-3953
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Volume 12, Issue 2 (Jun 2004)

Issues

Analysis of two-scale finite volume element method for elliptic problem

V. Ginting
  • Department of Mathematics, Texas A&M University, College Station, TX 77843-3404

In this paper we propose and analyze a class of finite volume element method for solving a second order elliptic boundary value problem whose solution is defined in more than one length scales. The method has the ability to incorporate the small scale behaviors of the solution on the large scale one. This is achieved through the construction of the basis functions on each element that satisfy the homogeneous elliptic differential equation. Furthermore, the method enjoys numerical conservation feature which is highly desirable in many applications. Existing analyses on its finite element counterpart reveal that there exists a resonance error between the mesh size and the small length scale. This result motivates an oversampling technique to overcome this drawback. We develop an analysis of the proposed method under the assumption that the coefficients are of two scales and periodic in the small scale. The theoretical results are confirmed experimentally by several convergence tests. Moreover, we present an application of the method to flows in porous media.

Key Words: Multiscale method,; finite volume element,; flow in porous media

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Published in Print: 2004-06-01


Citation Information: Journal of Numerical Mathematics jnma, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: https://doi.org/10.1515/156939504323074513.

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