We present new a posteriori error estimates for the finite volume approximations of elliptic problems. They are obtained by applying functional a posteriori error estimates to natural extensions of the approximate solution and its flux computed by the finite volume method. The estimates give guaranteed upper bounds for the errors in terms of the primal (energy) norm, dual norm (for fluxes), and...

In this article we propose and analyze an a posteriori error estimator for a three-field model of a generalized Stokes problem. The components of the a posteriori error estimator are defined via a non-linear projection of the residues of the variational equations. Both upper and lower bounds for the approximation error are derived in terms of the components of the a posteriori error estimator. ...

This paper deals with a general framework for a posteriori error estimates in boundary element methods which is specified for three examples, namely Symm's integral equation, an integral equation with a hypersingular operator, and a boundary integral equation for a transmission problem. Based on these estimates, an analog of Eriksson and Johnson's adaptive finite element method is proposed for ...