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Numerical convergence on adaptive grids for control volume methods

โœ Scribed by S.K. Khattri; I. Aavatsmark

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
458 KB
Volume
24
Category
Article
ISSN
0749-159X

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โœฆ Synopsis

Abstract

An adaptive technique for controlโ€volume methods applied to second order elliptic equations in two dimensions is presented. The discretization method applies to initially Cartesian grids aligned with the principal directions of the conductivity tensor. The convergence behavior of this method is investigated numerically. For solutions with low Sobolev regularity, the found L^2^ convergence order is two for the potential and one for the flow density. The system of linear equations is better conditioned for the adaptive grids than for uniform grids. The test runs indicate that a pure fluxโ€based refinement criterion is preferable.ยฉ 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008

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