A Posteriori Error Estimates for Finite Volume Approximations

被引：4
|
作者：
Cochez-Dhondt, S. [1 ]
Nicaise, S. [1 ]
Repin, S. [2 ]
机构：
[1] Univ Valenciennes & Hainaut Cambresis, CNRS, LAMAV, FR 2956,ISTV, F-59313 Valenciennes 9, France
[2] VA Steklov Math Inst, St Petersburg 191023, Russia
来源：
MATHEMATICAL MODELLING OF NATURAL PHENOMENA | 2009年 / 4卷 / 01期
关键词：
finite volume methods; elliptic problems; a posteriori error estimates of the functional type; ELEMENT APPROXIMATIONS;
D O I：
10.1051/mmnp/20094105
中图分类号：
Q [生物科学];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
We present new a posteriori error estimates for the finite volume approximations of elliptic problems. They are obtained by applying functional a posteriori error estimates to natural extensions of the approximate solution and its flux computed by the finite volume method. The estimates give guaranteed upper bounds for the errors in terms of the primal (energy) norm, dual norm (for fluxes), and also in terms of the combined primal-dual norms. It is shown that the estimates provide sharp upper and lower bounds of the error and their practical computation requires solving only finite-dimensional problems.
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页码：106 / 122
页数：17
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