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Convergence of a positive nonlinear control volume finite element scheme for an anisotropic seawater intrusion model with sharp interfaces
Author(s) -
Ait Hammou Oulhaj Ahmed,
Maltese David
Publication year - 2020
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22422
Subject(s) - nonlinear system , convergence (economics) , finite element method , finite volume method , mathematical analysis , mathematics , context (archaeology) , anisotropy , mechanics , geology , physics , thermodynamics , paleontology , quantum mechanics , economics , economic growth
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.