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Convergence of a positive nonlinear control volume finite element scheme for an anisotropic seawater intrusion model with sharp interfaces |
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| Authors: | Ahmed Ait Hammou Oulhaj David Maltese |
| Institution: | 1. Département Génie Informatique, Laboratoire de Mathématiques Appliquées de Compiègne, Centre de Recherches de Royallieu, Compiègne Cedex, France;2. Institut Polytechnique des Sciences Avancées, Ivrysur-Seine, France
Inria, University of Lille, CNRS, UMR 8524 3. – 4. Laboratoire Paul Painlevé, Lille, France |
| Abstract: | We study a sharp interface model in the context of seawater intrusion in an anisotropic unconfined aquifer. It is a degenerate parabolic system with cross-diffusion modeling the flow of fresh and saltwater. We study a nonlinear control volume finite element scheme. This scheme ensures the nonnegativity of the discrete solution without any restriction on the transmissibility coefficients. Moreover, it also provides a control on the entropy. The existence of a discrete solution and the convergence of this scheme are obtained, based on nonlinear stability results. |
| Keywords: | anisotropic porous media control of the entropy cross-diffusion nonlinear discretization numerical analysis seawater intrusion unconfined aquifer |