The paper is concerned with the Barenblatt-Biott model in the theory of poroelasticity. We derive a guaranteed estimate of the difference between exact and approximate solutions expressed in a combined norm that encompasses errors for the pressure fields computed from the diffusion part of the model and errors related to stresses (strains) of the elastic part. Estimates do not contain generic (mesh-dependent) constants and are valid for any conforming approximation of pressure and stress fields.
@article{arxiv.1003.5290,
title = {A posteriori error estimates for approximate solutions of Barenblatt-Biot poroelastic model},
author = {J. M. Nordbotten and T. Rahman and S. I. Repin and J. Valdman},
journal= {arXiv preprint arXiv:1003.5290},
year = {2010}
}