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An expanded mixed covolume method for elliptic problems

✍ Scribed by Hongxing Rui; Tongchao Lu

Publisher: John Wiley and Sons
Year: 2004
Tongue: English
Weight: 141 KB
Volume: 21
Category: Article
ISSN: 0749-159X
DOI: 10.1002/num.20024

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✦ Synopsis

Abstract

We consider the mixed covolume method combining with the expanded mixed element for a system of first‐order partial differential equations resulting from the mixed formulation of a general self‐adjoint elliptic problem with a full diffusion tensor. The system can be used to model the transport of a contaminant carried by a flow in porous media. We use the lowest order Raviart‐Thomas mixed element space. We show the first‐order error estimate for the approximate solution in L^2^ norm. We show the superconvergence both for pressure and velocity in certain discrete norms. We also get a finite difference scheme by using proper approximate integration formulas. Finally we give some numerical examples. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005

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