Fully mixed virtual element schemes for steady-state poroelastic stress-assisted diffusion
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914091447091200 |
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| author | Bermudez, Isaac Gomez-Vargas, Bryan Rubiano, Andres E. Ruiz-Baier, Ricardo |
| author_facet | Bermudez, Isaac Gomez-Vargas, Bryan Rubiano, Andres E. Ruiz-Baier, Ricardo |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_12307 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fully mixed virtual element schemes for steady-state poroelastic stress-assisted diffusion Bermudez, Isaac Gomez-Vargas, Bryan Rubiano, Andres E. Ruiz-Baier, Ricardo Numerical Analysis 65N30, 65N15, 74D05 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. |
| title | Fully mixed virtual element schemes for steady-state poroelastic stress-assisted diffusion |
| topic | Numerical Analysis 65N30, 65N15, 74D05 |
| url | https://arxiv.org/abs/2510.12307 |