@article{6fb0ed39f0a54871aaea7d7a50d32812,
title = "Twofold Saddle-Point Formulation of Biot Poroelasticity with Stress-Dependent Diffusion",
abstract = "We present a new stress/total-pressure formulation for poroelasticity that incorporates the coupling with steady nonlinear diffusion modified by stress. This nonlinear problem is written in mixed-primal form, which combines a perturbed twofold saddle-point system with an elliptic problem. We analyze the continuous formulation within the framework of abstract fixed-point theory and Fredholm alternative for compact operators. A mixed finite element method is proposed, and its stability and convergence are rigorously analyzed. We also provide a few representative numerical examples to illustrate the effectiveness of the proposed formulation. The resulting model can be used to study the steady case of waste removal in the brain, providing insight into the transport of solutes in poroelastic structures under the influence of stress.",
keywords = "mixed finite elements, perturbed saddle-point, poroelasticity, stress-altered diffusion",
author = "Bryan G{\'o}mez-Vargas and Mardal, {Kent Andr{\'e}} and Ricardo Ruiz-Baier and Vegard Vinje",
note = "Funding Information: The work of the first author was supported by the Vicerrector{\'i}a de Investigaci{\'o}n project 540-C0-202, Sede de Occidente, Universidad de Costa Rica. The work of the second author was supported by the Research Council of Norway grants 300305 and 301013. The work of the third author was supported by the Monash Mathematics Research Fund grant S05802-3951284, by the Australian Research Council through the Future Fellowship grant FT220100496 and Discovery Project grant DP22010316, and by the Ministry of Science and Higher Education of the Russian Federation within the framework of state support for the creation and development of World-Class Research Centers Digital biodesign and personalized healthcare grant 075-15-2022-304. Funding Information: *Received by the editors September 30, 2021; accepted for publication (in revised form) February 6, 2023; published electronically June 12, 2023. https://doi.org/10.1137/21M1449695 Funding: The work of the first author was supported by the Vicerrector\{\'i}a de Investigaci\o'n project 540-C0-202, Sede de Occidente, Universidad de Costa Rica. The work of the second author was supported by the Research Council of Norway grants 300305 and 301013. The work of the third author was supported by the Monash Mathematics Research Fund grant S05802-3951284, by the Australian Research Council through the Future Fellowship grant FT220100496 and Discovery Project grant DP22010316, and by the Ministry of Science and Higher Education of the Russian Federation within the framework of state support for the creation and development of World-Class Research Centers Digital biodesign and personalized healthcare grant 075-15-2022-304. Publisher Copyright: Copyright {\textcopyright} by SIAM.",
year = "2023",
doi = "10.1137/21m1449695",
language = "English",
volume = "61",
pages = "1449--1481",
journal = "SIAM Journal on Numerical Analysis",
issn = "0036-1429",
publisher = "Society for Industrial & Applied Mathematics (SIAM)",
number = "3",
}