Math. Model. Nat. Phenom.
Volume 4, Number 1, 2009Modelling and numerical methods in contact mechanics
|Page(s)||106 - 122|
|Published online||27 January 2009|
A Posteriori Error Estimates for Finite Volume Approximations
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
Corresponding author: firstname.lastname@example.org
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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