Error estimates for a mixed finite element discretization of some degenerate parabolic equations |
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Authors: | Florin A Radu Iuliu Sorin Pop Peter Knabner |
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Institution: | (1) Max-Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany;(2) UFZ, Helmholtz Center for Environmental Research, Permoserstr. 15, 04318 Leipzig, Germany;(3) Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;(4) Institute of Applied Mathematics, University Erlangen-Nürnberg, Martensstr. 3, 91058 Erlangen, Germany |
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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 one step implicit in time. The lowest order Raviart–Thomas elements
are used. Here we extend the results in Radu et al. (SIAM J Numer Anal 42:1452–1478, 2004), Schneid et al. (Numer Math 98:353–370,
2004) to a more general framework, by allowing for both types of degeneracies. We derive error estimates in terms of the discretization
parameters and show the convergence of the scheme. The features of the MFEM, especially of the lowest order Raviart–Thomas
elements, are now fully exploited in the proof of the convergence. The paper is concluded by numerical examples. |
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Keywords: | 65M12 65M15 65M60 35K65 35K55 76S05 |
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