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A Posteriori Error Estimates for Finite Volume Approximations
Published online by Cambridge University Press: 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.
- Type
- Research Article
- Information
- Mathematical Modelling of Natural Phenomena , Volume 4 , Issue 1: Modelling and numerical methods in contact mechanics , 2009 , pp. 106 - 122
- Copyright
- © EDP Sciences, 2009
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