Published

Cell conservative flux recovery and a posteriori error estimate of vertex-centered finite volume methods

Ming Wang and Long Chen

Advances in Applied Mathematics and Mechanics, 5 (5), 705-727, 2013.

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ABSTRACT:

 A cell conservative flux recovery technique is developed 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 obtained in this article
is apparently the first results on a posteriori error estimators for
high order finite volume methods.