Convergence of a positive nonlinear control volume finite element scheme for an anisotropic seawater intrusion model with sharp interfaces

被引：3
|
作者：
Oulhaj, Ahmed Ait Hammou [1 ]
Maltese, David [2 ,3 ]
机构：
[1] Ctr Rech Royallieu, Lab Math Appl Compiegne, Dept Genie Informat, BP 20529, F-60205 Compiegne, France
[2] Inst Polytech Sci Avancees, Ivrysur Seine, France
[3] Univ Lille, CNRS, UMR 8524, Inria,Lab Paul Painleve, Lille, France
来源：
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2020年 / 36卷 / 01期
关键词：
anisotropic porous media; control of the entropy; cross-diffusion; nonlinear discretization; numerical analysis; seawater intrusion; unconfined aquifer; CROSS-DIFFUSION; FLOWS; DERIVATION; STABILITY; EXISTENCE; GRAVITY;
D O I：
10.1002/num.22422
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：133 / 153
页数：21
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