Cell Conservative Flux Recovery and a Posteriori Error Estimate of Vertex-Centered Finite Volume Methods (Advances in Applied Mathematics and Mechanics, 2013)
A cell conservative flux recovery technique is developed here for vertex-centeredfinite volume methods of second order elliptic equations.It is based on solving a local Neumann problem on each control volume using mixedfinite element methods. The recovered flux is used toconstruct a constant free a posteriori error estimator which is proven to bereliable and efficient. Some numerical tests are presentedto confirm the theoretical results. Our method works for general order finite volumemethods and the recovery-based and residual-baseda posteriori error estimators are the first result ona posteriori error estimators for highorder finite volume methods.