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Issue Math. Model. Nat. Phenom.
Volume 4, Number 1, 2009
Modelling and numerical methods in contact mechanics
Page(s) 106 - 122
DOI 10.1051/mmnp/20094105
Published online 27 January 2009

Math. Model. Nat. Phenom. Vol. 4, No. 1, 2009, pp. 106-122
DOI: 10.1051/mmnp/20094105

A Posteriori Error Estimates for Finite Volume Approximations

S. Cochez-Dhondt1, S. Nicaise1 and S. Repin2

1  Université de Valenciennes et du Hainaut Cambrésis, LAMAV, FR CNRS 2956, ISTV, F59313 - Valenciennes Cedex 9, France
2  Steklov Institute of Mathematics in St. Petersburg, Fontanka 27, 191023, St. Petersburg, Russia

snicaise@univ-valenciennes.fr

Published online: 27 January 2009

Abstract
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.


Mathematics Subject Classification. 65N30

Key words: finite volume methods -- elliptic problems -- a posteriori error estimates of the functional type


© EDP Sciences 2009


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