A Posteriori Error Estimates for Approximate Solutions of the Barenblatt-Biot Poroelastic Model

Abstract

The paper is concerned with the Barenblatt-Biot model in the theory of poroelasticity. We derive a guaranteed estimate of the difference between exact and approximate solutions 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 the pressure and stress fields. © 2010, Institute of Mathematics, NAS of Belarus. All rights reserved.