Geodesic
A Posteriori Error Estimates for Finite Volume Approximations
S. Cochez-Dhondt1 ; S. Nicaise1 ; 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
Mathematical modelling of natural phenomena, Tome 4 (2009) no. 1, pp. 106-122.

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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.
DOI : 10.1051/mmnp/20094105

S. Cochez-Dhondt 1 ; S. Nicaise 1 ; S. Repin 2

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 
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S. Cochez-Dhondt; S. Nicaise; S. Repin. A Posteriori Error Estimates for Finite Volume Approximations. Mathematical modelling of natural phenomena, Tome 4 (2009) no. 1, pp. 106-122. doi : 10.1051/mmnp/20094105. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20094105/

[1] A. Agouzal, F. Oudin. A posteriori error estimator for finite volume methods. C. R. Acad. Sci. Paris, Sér. 1, 343 (2006), 349–354.

[2] S. Repin, S. Sauter, A. Smolianski. Two-Sided a posteriori error estimates for mixed formulations of elliptic problems. Preprint 21-2005, Institute of Mathematics, University of Zurich (to appear in SIAM J. Numer. Anal.).

[3] R. Verfürth. A review of a posteriori error estimation and adaptive mesh–refinement techniques. Wiley, Teubner, New York, 1996.

[4] M. Vohralík ESAIM: Proc. 2007 57 69

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