Comptes Rendus
no. S1
Numerical analysis of an incompressible soft material poromechanics model using T-coercivity
Mathieu Barré1, 2 ; Céline Grandmont3, 4, 5 ; Philippe Moireau6, 2 
1 Inria, 1 Rue Honoré d’Estienne d’Orves, 91120 Palaiseau, France
2 LMS, École Polytechnique, CNRS, Institut Polytechnique de Paris, Route de Saclay, 91120 Palaiseau, France
3 Inria, 2 Rue Simone Iff, 75012 Paris, France
4 LJLL, Sorbonne Université, CNRS, 4 Place Jussieu, 75005 Paris, France
5 Département de Mathématique, Université Libre de Bruxelles, CP 214, Boulevard du Triomphe, 1050 Bruxelles, Belgium
6 Inria, Batiment Alan Turing, 1 Rue Honoré d’Estienne d’Orves, Campus de l’École Polytechnique, 91120 Palaiseau, France
Comptes Rendus. Mécanique, Volume 351 (2023) no. S1, pp. 17-52.

This article is devoted to the numerical analysis of the full discretization of a generalized poromechanical model resulting from the linearization of an initial model fitted to soft tissue perfusion. Our strategy here is based on the use of energy-based estimates and T-coercivity methods, so that the numerical analysis benefits from the essential tools used in the existence analysis of the continuous-time and continuous-space formulation. In particular, our T-coercivity strategy allows us to obtain the necessary inf-sup condition for the global system from the inf-sup condition restricted to a subsystem having the same structure as the Stokes problem. This allows us to prove that any finite element pair adapted to the Stokes problem is also suitable for this global poromechanical model regardless of porosity and permeability, generalizing previous results from the literature studying this model.

Reçu le :
Accepté le :
Première publication :
Publié le :
DOI : 10.5802/crmeca.194
Mots clés : Poromechanics, mixture theory, incompressible limit, total discretization, inf-sup stability, energy preserving time-scheme
Mathieu Barré 1, 2 ; Céline Grandmont 3, 4, 5 ; Philippe Moireau 6, 2

1 Inria, 1 Rue Honoré d’Estienne d’Orves, 91120 Palaiseau, France
2 LMS, École Polytechnique, CNRS, Institut Polytechnique de Paris, Route de Saclay, 91120 Palaiseau, France
3 Inria, 2 Rue Simone Iff, 75012 Paris, France
4 LJLL, Sorbonne Université, CNRS, 4 Place Jussieu, 75005 Paris, France
5 Département de Mathématique, Université Libre de Bruxelles, CP 214, Boulevard du Triomphe, 1050 Bruxelles, Belgium
6 Inria, Batiment Alan Turing, 1 Rue Honoré d’Estienne d’Orves, Campus de l’École Polytechnique, 91120 Palaiseau, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Mathieu Barré; Céline Grandmont; Philippe Moireau. Numerical analysis of an incompressible soft material poromechanics model using $\tt {T}$-coercivity. Comptes Rendus. Mécanique, Volume 351 (2023) no. S1, pp. 17-52. doi : 10.5802/crmeca.194. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.194/

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