Hierarchical error estimates for finite volume approximation solution of elliptic equations

Authors:
Qingsong Zou
Affiliations:
Sun Yat-sen University, Department of Scientific Computation and Computer Applications, Guangzhou 510275, PR China
Venue:
Applied Numerical Mathematics
Year:
2010

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Abstract

We propose hierarchical error estimates for the vertex-centered finite volume approximation solution of elliptic equations. The reliability and efficiency of hierarchical estimates are analyzed by showing that the H^1-norm of the finite volume approximate error are equivalent to our hierarchical estimator up to some oscillation terms which are supposed to be high order terms. Moreover, we show that the small oscillation implies the saturation property, as what has been proved for finite elements approximation in Dorfler and Nochetto (2002) [16]. Numerical experiments confirm our theoretic findings.