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.