Year: 2010
International Journal of Numerical Analysis and Modeling, Vol. 7 (2010), Iss. 1 : pp. 1–29
Abstract
The goal of this article is to study the stability and the convergence of cell-centered finite volumes (FV) in a domain $\Omega= (0,1)\times(0,1)\subset R^2$ with non-uniform rectangular control volumes. The discrete FV derivatives are obtained using the Taylor Series Expansion Scheme (TSES), (see [4] and [10]), which is valid for any quadrilateral mesh. Instead of using compactness arguments, the convergence of the FV method is obtained by comparing the FV method to the associated finite differences (FD) scheme. As an application, using the FV discretizations, convergence results are proved for elliptic equations with Dirichlet boundary condition.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2010-IJNAM-708
International Journal of Numerical Analysis and Modeling, Vol. 7 (2010), Iss. 1 : pp. 1–29
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Finite volume methods finite difference methods Taylor series expansion scheme (TSES) convergence and stability elliptic equations.