Error estimates for the finite volume discretization for the porous medium equation

Authors:
I. S. Pop;M. Sepúlveda;F. A. Radu;O. P. Vera Villagrán
Affiliations:
CASA, TU Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;CI2MA, Universidad de Concepción, Casilla 160-C, Concepción, Chile;UFZ-Helmholtz Center for Environmental Research, Permoserstr. 15, D-04318 Leipzig, Germany and University of Jena, Wöllnitzerstr. 7, D-07749, Jena, Germany;Universidad del Bío-Bío, Collao 1202, Casilla 5-C, Concepción, Chile
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 7
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Abstract

We analyze the convergence of a numerical scheme for a class of degenerate parabolic problems modelling reactions in porous media, and involving a nonlinear, possibly vanishing diffusion. The scheme involves the Kirchhoff transformation of the regularized nonlinearity, as well as an Euler implicit time stepping and triangle based finite volumes. We prove the convergence of the approach by giving error estimates in terms of the discretization and regularization parameter.