Numerical analysis of an incompressible soft material poromechanics model using $\tt {T}$-coercivity
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 $\tt {T}$-coercivity methods, s...
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Académie des sciences
2023-06-01
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| Series: | Comptes Rendus. Mécanique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.194/ |
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| author | Barré, Mathieu Grandmont, Céline Moireau, Philippe |
| author_facet | Barré, Mathieu Grandmont, Céline Moireau, Philippe |
| author_sort | Barré, Mathieu |
| collection | DOAJ |
| description | 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 $\tt {T}$-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 $\tt {T}$-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. |
| format | Article |
| id | doaj-art-48ae1f979c1f4c13964186d36db826a9 |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2023-06-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-48ae1f979c1f4c13964186d36db826a92025-02-07T13:46:20ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342023-06-01351S1175210.5802/crmeca.19410.5802/crmeca.194Numerical analysis of an incompressible soft material poromechanics model using $\tt {T}$-coercivityBarré, Mathieu0Grandmont, Céline1Moireau, Philippe2Inria, 1 Rue Honoré d’Estienne d’Orves, 91120 Palaiseau, France; LMS, École Polytechnique, CNRS, Institut Polytechnique de Paris, Route de Saclay, 91120 Palaiseau, FranceDépartement de Mathématique, Université Libre de Bruxelles, CP 214, Boulevard du Triomphe, 1050 Bruxelles, Belgium; Inria, 2 Rue Simone Iff, 75012 Paris, France; LJLL, Sorbonne Université, CNRS, 4 Place Jussieu, 75005 Paris, FranceInria, Batiment Alan Turing, 1 Rue Honoré d’Estienne d’Orves, Campus de l’École Polytechnique, 91120 Palaiseau, France; LMS, École Polytechnique, CNRS, Institut Polytechnique de Paris, Route de Saclay, 91120 Palaiseau, FranceThis 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 $\tt {T}$-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 $\tt {T}$-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.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.194/Poromechanicsmixture theoryincompressible limittotal discretizationinf-sup stabilityenergy preserving time-scheme |
| spellingShingle | Barré, Mathieu Grandmont, Céline Moireau, Philippe Numerical analysis of an incompressible soft material poromechanics model using $\tt {T}$-coercivity Comptes Rendus. Mécanique Poromechanics mixture theory incompressible limit total discretization inf-sup stability energy preserving time-scheme |
| title | Numerical analysis of an incompressible soft material poromechanics model using $\tt {T}$-coercivity |
| title_full | Numerical analysis of an incompressible soft material poromechanics model using $\tt {T}$-coercivity |
| title_fullStr | Numerical analysis of an incompressible soft material poromechanics model using $\tt {T}$-coercivity |
| title_full_unstemmed | Numerical analysis of an incompressible soft material poromechanics model using $\tt {T}$-coercivity |
| title_short | Numerical analysis of an incompressible soft material poromechanics model using $\tt {T}$-coercivity |
| title_sort | numerical analysis of an incompressible soft material poromechanics model using tt t coercivity |
| topic | Poromechanics mixture theory incompressible limit total discretization inf-sup stability energy preserving time-scheme |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.194/ |
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