Monotone corrections for generic cell-centered finite volume approximations of anisotropic diffusion equations

We present a nonlinear technique to correct a general finite volume scheme for anisotropic diffusion problems, which provides a discrete maximum principle. We point out general properties satisfied by many finite volume schemes and prove the proposed corrections also preserve these properties. We th...

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Bibliographic Details
Published in:Numerische Mathematik 2013-11, Vol.125 (3), p.387-417
Main Authors: Cancès, Clément, Cathala, Mathieu, Le Potier, Christophe
Format: Article
Language:English
Subjects:
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
Simulation
Theoretical
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Summary:We present a nonlinear technique to correct a general finite volume scheme for anisotropic diffusion problems, which provides a discrete maximum principle. We point out general properties satisfied by many finite volume schemes and prove the proposed corrections also preserve these properties. We then study two specific corrections proving, under numerical assumptions, that the corresponding approximate solutions converge to the continuous one as the size of the mesh tends to zero. Finally we present numerical results showing that these corrections suppress local minima produced by the original finite volume scheme.
ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-013-0545-5