A semi-implicit monotone difference scheme for an initial-boundary value problem of a strongly degenerate parabolic equation modeling sedimentation-consolidation processes

Bürger, Raimund; Coronel, Aníbal; Sepúlveda, Mauricio

doi:10.1090/S0025-5718-05-01787-4

A semi-implicit monotone difference scheme for an initial-boundary value problem of a strongly degenerate parabolic equation modeling sedimentation-consolidation processes
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by Raimund Bürger, Aníbal Coronel and Mauricio Sepúlveda;

Math. Comp. 75 (2006), 91-112

DOI: https://doi.org/10.1090/S0025-5718-05-01787-4

Published electronically: October 21, 2005

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Abstract:

We prove the convergence of a semi-implicit monotone finite difference scheme approximating an initial-boundary value problem for a spatially one-dimensional quasilinear strongly degenerate parabolic equation, which is supplied with two different inhomogeneous flux-type boundary conditions. This problem arises in the modeling of the sedimentation-consolidation process. We formulate the definition of entropy solution of the model in the sense of Kru$\check {\mbox {z}}$kov and prove convergence of the scheme to the unique $BV$ entropy solution of the problem, up to satisfaction of one of the boundary conditions.

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