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 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.

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