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 -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 -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.
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Mathieu Barré 1, 2 ; Céline Grandmont 3, 4, 5 ; Philippe Moireau 6, 2
@article{CRMECA_2023__351_S1_17_0, author = {Mathieu Barr\'e and C\'eline Grandmont and Philippe Moireau}, title = {Numerical analysis of an incompressible soft material poromechanics model using $\tt {T}$-coercivity}, journal = {Comptes Rendus. M\'ecanique}, pages = {17--52}, publisher = {Acad\'emie des sciences, Paris}, volume = {351}, number = {S1}, year = {2023}, doi = {10.5802/crmeca.194}, language = {en}, }
TY - JOUR AU - Mathieu Barré AU - Céline Grandmont AU - Philippe Moireau TI - Numerical analysis of an incompressible soft material poromechanics model using $\tt {T}$-coercivity JO - Comptes Rendus. Mécanique PY - 2023 SP - 17 EP - 52 VL - 351 IS - S1 PB - Académie des sciences, Paris DO - 10.5802/crmeca.194 LA - en ID - CRMECA_2023__351_S1_17_0 ER -
%0 Journal Article %A Mathieu Barré %A Céline Grandmont %A Philippe Moireau %T Numerical analysis of an incompressible soft material poromechanics model using $\tt {T}$-coercivity %J Comptes Rendus. Mécanique %D 2023 %P 17-52 %V 351 %N S1 %I Académie des sciences, Paris %R 10.5802/crmeca.194 %G en %F CRMECA_2023__351_S1_17_0
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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