Volume 5, Issue 5
Cell Conservative Flux Recovery and A Posteriori Error Estimate of Vertex-Centered Finite Volume Methods

Long Chen & Ming Wang

Adv. Appl. Math. Mech., 5 (2013), pp. 705-727.

Published online: 2013-05

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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

Finite volume methods flux recovery a posteriori error estimates

  • AMS Subject Headings

65N15 65N30 65N50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-5-705, author = {Long Chen and Ming Wang}, title = {Cell Conservative Flux Recovery and A Posteriori Error Estimate of Vertex-Centered Finite Volume Methods}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2013}, volume = {5}, number = {5}, pages = {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 is the first result on a posteriori error estimators for high order finite volume methods.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.12-m1279}, url = {http://global-sci.org/intro/article_detail/aamm/93.html} }
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