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MiS Preprint
12/2007

Error estimates for a mixed finite element discretization of some degenerate parabolic equations

Florin Adrian Radu, Iuliu Sorin Pop and Peter Knabner

Abstract

We consider a numerical scheme for a class of degenerate parabolic equations, including both slow and fast diffusion cases. A particular example in this sense is the Richards' equation modeling the flow in porous media. The numerical scheme is based on the mixed finite element method (MFEM) in space, and is of first order implicit in time. The lowest order Raviart-Thomas elements are used. We derive error estimates in terms of the discretization parameters and show the convergence of the scheme. The paper is concluded by numerical examples.

Received:
Jan 30, 2007
Published:
Jan 30, 2007
MSC Codes:
65M60, 65M12, 35K65
Keywords:
mixed finite element method, error estimates, degenerate parabolic equations, porous media

Related publications

inJournal
2008 Journal Open Access
Florin Adrian Radu, Sorin Pop and Peter Knabner

Error estimates for a mixed finite element discretization of some degenerate parabolic equations

In: Numerische Mathematik, 109 (2008) 2, pp. 285-311