Error estimates for a mixed finite element discretization of some degenerate parabolic equations
Florin Adrian Radu, Iuliu Sorin Pop, and Peter Knabner
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Submission date: 30. Jan. 2007
published in: Numerische Mathematik, 109 (2008) 2, p. 285-311
DOI number (of the published article): 10.1007/s00211-008-0139-9
MSC-Numbers: 65M60, 65M12, 35K65
Keywords and phrases: mixed finite element method, error estimates, degenerate parabolic equations, porous media
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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.