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J. Droniou

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

Keywords: convection?diffusion equations, finite volume, convergence rate, interpolation

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 of Numerical Mathematics, Walter de Gruyter

Print ISSN: 1570-2820
Volume: 11, 03/2003
Pages: 1 - 32

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