A posteriori error estimates for approximate solutions of Barenblatt-Biot poroelastic model

TL;DR

This paper develops guaranteed a posteriori error estimates for approximate solutions of the Barenblatt-Biot poroelastic model, providing bounds on errors in pressure and stress fields without mesh-dependent constants.

Contribution

It introduces a novel, guaranteed error estimation method applicable to any conforming approximation in the Barenblatt-Biot model, enhancing accuracy assessment in poroelasticity simulations.

Findings

Error estimates are mesh-independent.

Estimates cover both pressure and stress errors.

Applicable to any conforming approximation.

Abstract

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.