Mixed Finite Element Method and numerical analysis of a\n convection-diffusion-reaction model in a porous medium

2020/06/03 by Éloïse Comte, Comte, Éloïse
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2006.02502

openalex publication_date 2020/06/03 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

A hydrogeological model for the spread of pollution in an aquifer is\nconsidered. The model consists in a convection-diffusion-reaction equation\ninvolving the dispersion tensor which depends nonlinearly of the fluid\nvelocity. We introduce an explicit flux in the model and use a mixed Finite\nElement Method for the discretization. We provide existence, uniqueness and\nstability results for the discrete model. A convergence result is obtained for\nthe semi-discretized in time problem and for the fully discretization.\n

Citations

• A priori and a posteriori analysis of finite volume discretizations of Darcy?s equations

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