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.

引用

页码：106 / 122

页数：17

共 50 条

[31] Error estimates for finite volume element methods for general second-order elliptic problems [J].

Wu, HJ ;

Li, RH .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2003, 19 (06) :693-708

[32] On pointwise error estimates for Voronoi-based finite volume methods for the Poisson equation on the sphere [J].

Poveda, Leonardo A. A. ;

Peixoto, Pedro .

ADVANCES IN COMPUTATIONAL MATHEMATICS, 2023, 49 (03)

[33] Goal-oriented a posteriori error estimation for conforming and nonconforming approximations with inexact solvers [J].

Mallik, Gouranga ;

Vohralik, Martin ;

Yousef, Soleiman .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2020, 366

[34] A posteriori error estimates, stopping criteria, and adaptivity for two-phase flows [J].

Vohralik, Martin ;

Wheeler, Mary F. .

COMPUTATIONAL GEOSCIENCES, 2013, 17 (05) :789-812

[35] A POSTERIORI ERROR ESTIMATES FOR ELLIPTIC PROBLEMS WITH DIRAC MEASURE TERMS IN WEIGHTED SPACES [J].

Pablo Agnelli, Juan ;

Garau, Eduardo M. ;

Morin, Pedro .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2014, 48 (06) :1557-1581

[36] An a posteriori error estimator for the mimetic finite difference approximation of elliptic problems [J].

da Veiga, Lourenco Beirao ;

Manzini, Gianmarco .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2008, 76 (11) :1696-1723

[37] Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics [J].

Derigs D. ;

Gassner G.J. ;

Walch S. ;

Winters A.R. .

Jahresbericht der Deutschen Mathematiker-Vereinigung, 2018, 120 (3) :153-219

[38] ERROR ESTIMATES FOR DISCRETE GENERALIZED FEMS WITH LOCALLY OPTIMAL SPECTRAL APPROXIMATIONS [J].

Ma, Chupeng ;

Scheichl, Robert .

MATHEMATICS OF COMPUTATION, 2022, 91 (338) :2539-2569

[39] A framework for obtaining guaranteed error bounds for finite element approximations [J].

Ainsworth, Mark .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2010, 234 (09) :2618-2632

[40] TWO-SIDE A POSTERIORI ERROR ESTIMATES FOR THE DUAL-WEIGHTED RESIDUAL METHOD [J].

Endtmayer, B. ;

Langer, U. ;

Wick, T. .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2020, 42 (01) :A371-A394

← 1 2 3 4 5 →