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Article Dans Une Revue Numerical Methods for Partial Differential Equations Année : 2020

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

Résumé

We consider a degenerate parabolic system modelling the flow of fresh and saltwater in an anisotropic porous medium in the context of seawater intrusion. We propose and analyze a nonlinear Control Volume Finite Element scheme. This scheme ensures the nonnegativity of the discrete solution without any restriction on the mesh and on the anisotropy tensor. Moreover It also provides a control on the entropy. Based on these nonlinear stability results, we show that the scheme converges towards a weak solution to the problem. Numerical results are provided to illustrate the behavior of the model and of the scheme.
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Dates et versions

hal-01906872 , version 2 (03-11-2018)

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Ahmed Ait Hammou Oulhaj, David Maltese. Convergence of a positive nonlinear control volume finite element scheme for an anisotropic seawater intrusion model with sharp interfaces. Numerical Methods for Partial Differential Equations, 2020, 36 (1), pp.133-153. ⟨10.1002/num.22422⟩. ⟨hal-01906872⟩
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