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Title: | Global existence of weak solutions to unsaturated poroelasticity | Authors: | BOTH, Jakub POP, Sorin Yotov, Ivan |
Issue Date: | 2021 | Publisher: | EDP SCIENCES S A | Source: | ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 55 (6) , p. 2849 -2897, | Abstract: | We study unsaturated poroelasticity, i.e., coupled hydro-mechanical processes in variably saturated porous media, here modeled by a non-linear extension of Biot's well-known quasi-static consolidation model. The coupled elliptic-parabolic system of partial differential equations is a simplified version of the general model for multi-phase flow in deformable porous media, obtained under similar assumptions as usually considered for Richards' equation. In this work, existence of weak solutions is established in several steps involving a numerical approximation of the problem using a physically-motivated regularization and a finite element/finite volume discretization. Eventually, solvability of the original problem is proved by a combination of the Rothe and Galerkin methods, and further compactness arguments. This approach in particular provides the convergence of the numerical discretization to a regularized model for unsaturated poroelasticity. The final existence result holds under non-degeneracy conditions and natural continuity properties for the constitutive relations. The assumptions are demonstrated to be reasonable in view of geotechnical applications. | Notes: | Both, JW (corresponding author), Univ Bergen, Dept Math, Allegaten 41, N-5007 Bergen, Norway. jakub.both@uib.no |
Keywords: | Poroelasticity; Biot model; variably saturated porous media; Richards';equation | Document URI: | http://hdl.handle.net/1942/36267 | ISSN: | 2822-7840 | e-ISSN: | 2804-7214 | DOI: | 10.1051/m2an/2021063 | ISI #: | WOS:000723784400005 | Rights: | This journal is currently published in open access under a Subscribe-to-Open model (S2O). S | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2022 |
Appears in Collections: | Research publications |
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m2an200148.pdf | Published version | 1.63 MB | Adobe PDF | View/Open |
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