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
IMPACT FACTOR 2015: 0.552
5-year IMPACT FACTOR: 2.203
SCImago Journal Rank (SJR) 2015: 2.152
Source Normalized Impact per Paper (SNIP) 2015: 3.045
Impact per Publication (IPP) 2015: 3.022
Mathematical Citation Quotient (MCQ) 2015: 1.17
Analysis of two-scale finite volume element method for elliptic problem
∗ Department of Mathematics, Texas A&M University, College Station, TX 77843-3404
Citation Information: Journal of Numerical Mathematics jnma. Volume 12, Issue 2, Pages 119–141, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: 10.1515/156939504323074513, June 2004
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.
Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.