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Error estimates for mixed finite element discretization of the Richards equation
Author(s) -
Radu Florin A.
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810523
Subject(s) - discretization , finite element method , mathematics , convergence (economics) , degenerate energy levels , degeneracy (biology) , richards equation , nonlinear system , transformation (genetics) , scheme (mathematics) , mathematical analysis , physics , engineering , bioinformatics , biochemistry , chemistry , geotechnical engineering , quantum mechanics , biology , gene , economics , thermodynamics , water content , economic growth
We present a numerical scheme based on the mixed finite element method (MFEM) for the Richards equation, a nonlinear, degenerate parabolic equation. Due to the degeneracy, the solution of the equation has low regularity and therefore only lower order finite elements are recommended. We review the main posibilities for proving the convergence of the scheme. Especially for the case without using the Kirchhoff transformation a new result is given. We also briefly discuss how to solve the nonlinear fully discrete problems appearing at each time step and refer to papers where the convergence of these methods is rigurously studied. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)