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T. Gallouët, R. Herbin, M. Vignal (2000)
Error Estimates on the Approximate Finite Volume Solution of Convection Diffusion Equations with General Boundary ConditionsSIAM J. Numer. Anal., 37
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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 – de Gruyter
Published: Mar 1, 2003
Keywords: convection–diffusion equations,; Finite Volume,; convergence rate,; interpolation
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