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Cell Conservative Flux Recovery and A Posteriori Error Estimate of Vertex-Centered Finite Volume Methods

Published online by Cambridge University Press:  03 June 2015

Long Chen  and
Ming Wang
Long Chen*
Affiliation:
Department of Mathematics, University of California at Irvine, Irvine, CA 92697, USA
Ming Wang*
Affiliation:
LMAM, School of Mathematical Sciences, Peking University, Beijing 100080, China
*
Corresponding author. Email: chenlong@math.uci.edu
Email: wangming.pku@gmail.com
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Abstract

A cell conservative flux recovery technique is developed here for vertex-centered finite volume methods of second order elliptic equations. It is based on solving a local Neumann problem on each control volume using mixed finite element methods. The recovered flux is used to construct a constant free a posteriori error estimator which is proven to be reliable and efficient. Some numerical tests are presented to confirm the theoretical results. Our method works for general order finite volume methods and the recovery-based and residual-based a posteriori error estimators is the first result on a posteriori error estimators for high order finite volume methods.

Keywords

65N1565N3065N50Finite volume methodsflux recoverya posteriori error estimates
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 5 , Issue 5 , October 2013 , pp. 705 - 727
Copyright
Copyright © Global-Science Press 2013

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