Cell Conservative Flux Recovery and a Posteriori Error Estimate of Vertex-Centered Finite Volume Methods
Year: 2013
Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 5 : pp. 705–727
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 are the first result on a posteriori error estimators for high order finite volume methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.12-m1279
Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 5 : pp. 705–727
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Finite volume methods flux recovery a posteriori error estimates.
Author Details
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Encyclopedia of Computational Mechanics Second Edition
Finite Volume Methods: Foundation and Analysis
Barth, Timothy
Herbin, Raphaèle
Ohlberger, Mario
2017
https://doi.org/10.1002/9781119176817.ecm2010 [Citations: 10]