A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations

被引：66
|
作者：
Ohlberger, M [1 ]
机构：
[1] Univ Freiburg, Inst Angew Math, D-79104 Freiburg, Germany
来源：
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2001年 / 35卷 / 02期
关键词：
a posteriori error estimates; convection diffusion reaction equation; finite volume schemes; adaptive methods; unstructured grids;
D O I：
10.1051/m2an:2001119
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation c(t) + del . (uf(c)) (D delc)+ lambdac = 0. The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the L-1-norm, independent of the diffusion parameter D. The resulting a posteriori error estimate is used to define an grid adaptive solution algorithm for the finite volume scheme. Finally numerical experiments underline the applicability of the theoretical results.
引用
收藏
页码：355 / 387
页数：33
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