Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem

被引：3
|
作者：
Mehats, F [1 ]
机构：
[1] Univ Toulouse 3, MIP, UMR 5640, CNRS, F-31062 Toulouse 04, France
来源：
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2002年 / 36卷 / 06期
关键词：
oblique derivative boundary problem; finite difference scheme; heat equation; Burgers equation;
D O I：
10.1051/m2an:2003008
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present here a discretization of a nonlinear oblique derivative boundary value problem for the heat equation in dimension two. This finite difference scheme takes advantages of the structure of the boundary condition, which can be reinterpreted as a Burgers equation in the space variables. This enables to obtain an energy estimate and to prove the convergence of the scheme. We also provide some numerical simulations of this problem and a numerical study of the stability of the scheme, which appears to be in good agreement with the theory.
引用
收藏
页码：1111 / 1132
页数：22
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