Finite volume scheme and renormalized solutions for nonlinear elliptic Neumann problem with L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^1$$\end{document} data

被引：0
作者：
Mirella Aoun [1 ]
Olivier Guibé [1 ]
机构：
[1] Univ Rouen Normandie,
[2] CNRS,undefined
[3] Laboratoire de Mathématiques Raphaël Salem,undefined
[4] UMR 6085,undefined
来源：
Calcolo | 2024年 / 61卷 / 3期
关键词：
Convection-diffusion equation; Finite volume schemes; Renormalized solution; Neumann boundary conditions; Integrable data; Numerical analysis; 65N08; 65N12; 35J25;
D O I：
10.1007/s10092-024-00602-3
中图分类号：
学科分类号：
摘要：
In this paper we study the convergence of a finite volume approximation of a convective diffusive elliptic problem with Neumann boundary conditions and L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^1$$\end{document} data. To deal with the non-coercive character of the equation and the low regularity of the right hand-side we mix the finite volume tools and the renormalized techniques. To handle the Neumann boundary conditions we choose solutions having a null median and we prove a convergence result. We present also some numerical experiments in dimension 2 to illustrate the rate of convergence.
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