Cell centered finite volume methods using Taylor series expansion scheme without fictitious domains
Gung-Min Gie 1, Roger Temam 11 The Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 East Third Street, Bloomington, Indiana 47405, USA.
Received by the editors March 15, 2009.
The goal of this article is to study the stability and the convergence of cell-centered finite volumes (FV) in a domain $\Omega= (0; 1)x(0; 1)\subset R^2$ with non-uniform rectangular control volumes. The discrete FV derivatives are obtained using the Taylor Series Expansion Scheme (TSES), (see  and ), 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.
AMS subject classifications: 65N12, 65N25, 76M12, 76M20
Key words: Finite volume methods, finite difference methods, Taylor series expansion scheme (TSES), convergence and stability, elliptic equations.
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