Fully mixed virtual element schemes for steady-state poroelastic stress-assisted diffusion
Abstract
We propose a fully mixed virtual element method for the numerical approximation of the coupling between stress-altered diffusion and linear elasticity equations with strong symmetry of total poroelastic stress (using the Hellinger--Reissner principle). A novelty of this work is that we introduce a less restrictive assumption on the stress-assisted diffusion coefficient, requiring an analysis of the perturbed diffusion equation using Banach spaces. The solvability of the continuous and discrete problems is established using a suitable modification of the abstract theory for perturbed saddle-point problems in Banach spaces (which is in itself a new result of independent interest). In addition, we establish optimal a priori error estimates. The method and its analysis are robust with respect to the poromechanical parameters. We also include a number of numerical examples that illustrate the properties of the proposed scheme.
Cite
@article{arxiv.2510.12307,
title = {Fully mixed virtual element schemes for steady-state poroelastic stress-assisted diffusion},
author = {Isaac Bermudez and Bryan Gomez-Vargas and Andres E. Rubiano and Ricardo Ruiz-Baier},
journal= {arXiv preprint arXiv:2510.12307},
year = {2025}
}