Finite volume scheme and renormalized solutions for nonlinear elliptic Neumann problem with $$L^1$$ data

IF 1.4 2区数学 Q1 MATHEMATICS

Calcolo Pub Date : 2024-07-06 DOI:10.1007/s10092-024-00602-3

Mirella Aoun, Olivier Guibé

引用次数: 0

Abstract

In this paper we study the convergence of a finite volume approximation of a convective diffusive elliptic problem with Neumann boundary conditions and $L^1$ 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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具有 $L^1$$ 数据的非线性椭圆 Neumann 问题的有限体积方案和重规范化解

在本文中，我们研究了具有诺伊曼边界条件和 $L^1$ 数据的对流扩散椭圆问题的有限体积近似的收敛性。为了处理方程的非强制特性和右侧的低正则性，我们混合使用了有限体积工具和重正化技术。为了处理诺伊曼边界条件，我们选择了具有空中值的解，并证明了收敛结果。我们还介绍了维度 2 中的一些数值实验，以说明收敛速度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Calcolo 数学-数学

CiteScore

2.40

自引率

11.80%

发文量

审稿时长

>12 weeks

期刊介绍： Calcolo is a quarterly of the Italian National Research Council, under the direction of the Institute for Informatics and Telematics in Pisa. Calcolo publishes original contributions in English on Numerical Analysis and its Applications, and on the Theory of Computation. The main focus of the journal is on Numerical Linear Algebra, Approximation Theory and its Applications, Numerical Solution of Differential and Integral Equations, Computational Complexity, Algorithmics, Mathematical Aspects of Computer Science, Optimization Theory. Expository papers will also appear from time to time as an introduction to emerging topics in one of the above mentioned fields. There will be a "Report" section, with abstracts of PhD Theses, news and reports from conferences and book reviews. All submissions will be carefully refereed.