A Posteriori Error Estimates for Finite Volume Approximations

@inproceedings{CochezDhondt2009APE,
  title={A Posteriori Error Estimates for Finite Volume Approximations},
  author={Sarah Cochez-Dhondt and Serge Nicaise and Sergey Repin},
  year={2009}
}
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 also in terms of the combined primal–dual norms. It is shown that the estimates provide sharp upper… CONTINUE READING