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Error estimates for the convergence of a finite volume discretization of convection–diffusion equations

Error estimates for the convergence of a finite volume discretization of convection–diffusion... We study error estimates for a finite volume discretization of an elliptic equation. We prove that, for s ∈ 0, 1, if the exact solution belongs to H 1+ s and the right-hand side is ƒ +div( G ) with ƒ ∈ L 2 and G ∈ ( H s ) N , then the solution of the finite volume scheme converges in discrete H 1 - norm to the exact solution, with a rate of convergence of order h s (where h is the size of the mesh). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Numerical Mathematics de Gruyter

Error estimates for the convergence of a finite volume discretization of convection–diffusion equations

Journal of Numerical Mathematics , Volume 11 (1) – Mar 1, 2003

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References (14)

Publisher
de Gruyter
Copyright
Copyright 2003, Walter de Gruyter
ISSN
1570-2820
eISSN
1569-3953
DOI
10.1515/156939503322004873
Publisher site
See Article on Publisher Site

Abstract

We study error estimates for a finite volume discretization of an elliptic equation. We prove that, for s ∈ 0, 1, if the exact solution belongs to H 1+ s and the right-hand side is ƒ +div( G ) with ƒ ∈ L 2 and G ∈ ( H s ) N , then the solution of the finite volume scheme converges in discrete H 1 - norm to the exact solution, with a rate of convergence of order h s (where h is the size of the mesh).

Journal

Journal of Numerical Mathematicsde Gruyter

Published: Mar 1, 2003

Keywords: convection–diffusion equations,; Finite Volume,; convergence rate,; interpolation

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