| Issue |
Math. Model. Nat. Phenom.
Volume 4, Number 1, 2009
Modelling and numerical methods in contact mechanics
|
|
|---|---|---|
| Page(s) | 106 - 122 | |
| DOI | https://doi.org/10.1051/mmnp/20094105 | |
| Published online | 27 January 2009 | |
A Posteriori Error Estimates for Finite Volume Approximations
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
Corresponding author: snicaise@univ-valenciennes.fr
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.