We analyze residual and hierarchical
a posteriori error estimates for nonconforming finite element
approximations of elliptic problems with variable coefficients.
We consider a finite volume box scheme equivalent to
a nonconforming mixed finite element method in a Petrov–Galerkin
setting. We prove that
all the estimators yield global upper and local lower bounds for the discretization
error. Finally, we present results illustrating the efficiency of the
estimators, for instance, in the simulation of Darcy flows through
heterogeneous porous media.