Nonconforming finite element methods for a Stokes/Biot fluid–poroelastic structure interaction model

Houédanou, Koffi Wilfrid

doi:10.1016/j.rinam.2020.100127

Cited by 6 publications

(3 citation statements)

References 21 publications

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“…A second order in time decoupling scheme for a nonlinear Stokes-Biot model is developed in [39]. Recent works study various discretization schemes for the Stokes-Biot system, including a coupled discontinuous Galerkin -mixed finite element method [50], a staggered finite element method [14] and non-conforming finite element method [51].…”

Section: Introductionmentioning

confidence: 99%

A mixed elasticity formulation for fluid–poroelastic structure interaction

Yotov

2022

ESAIM: M2AN

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We develop a mixed finite element method for the coupled problem arising in the interaction between a free fluid governed by the Stokes equations and flow in deformable porous medium modeled by the Biot system of poroelasticity. Mass conservation, balance of stress, and the Beavers-Joseph-Saffman condition are imposed on the interface. We consider a fully mixed Biot formulation based on a weakly symmetric stress-displacement-rotation elasticity system and Darcy velocity-pressure flow formulation. A velocity-pressure formulation is used for the Stokes equations. The interface conditions are incorporated through the introduction of the traces of the structure velocity and the Darcy pressure as Lagrange multipliers. Existence and uniqueness of a solution are established for the continuous weak formulation. Stability and error estimates are derived for the semi-discrete continuous-in-time mixed finite element approximation. Numerical experiments are presented to verify the theoretical results and illustrate the robustness of the method with respect to the physical parameters.

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Section: Introductionmentioning

confidence: 99%

A mixed elasticity formulation for fluid–poroelastic structure interaction

Yotov

2022

ESAIM: M2AN

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“…We use the conditions proposed in [1] (although, other forms and dedicated phenomena could be incorporated without much effort, such as fluid entry resistance [2,3]). The recent literature contains various numerical methods for (Navier-)Stokes/Biot interface formulations including mixed, double mixed, monolithic, segregated, conforming, non-conforming, and DG discretizations [4,5,6,7,8,9,10,11,12,13,14,15].…”

Section: Scopementioning

confidence: 99%

Parameter-robust methods for the Biot-Stokes interfacial coupling without Lagrange multipliers

Boon,

Hornkjøl,

Kuchta

et al. 2021

Preprint

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In this paper we advance the analysis of discretizations for a fluid-structure interaction model of the monolithic coupling between the free flow of a viscous Newtonian fluid and a deformable porous medium separated by an interface. A five-field mixed-primal finite element scheme is proposed solving for Stokes velocitypressure and Biot displacement-total pressure-fluid pressure. Adequate inf-sup conditions are derived, and one of the distinctive features of the formulation is that its stability is established robustly in all material parameters. We propose robust preconditioners for this perturbed saddle-point problem using appropriately weighted operators in fractional Sobolev and metric spaces at the interface. The performance is corroborated by several test cases, including the application to interfacial flow in the brain.

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“…A second order in time decoupling scheme for a nonlinear Stokes-Biot model is developed in [34]. Recent works study various discretization schemes for the Stokes-Biot system, including a coupled discontinuous Galerkin -mixed finite element method [44], a staggered finite element method [14] and non-conforming finite element method [45].…”

Section: Introductionmentioning

confidence: 99%

A mixed elasticity formulation for fluid-poroelastic structure interaction

Li¹,

Yotov²

2020

Preprint

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We develop a mixed finite element method for the coupled problem arising in the interaction between a free fluid governed by the Stokes equations and flow in deformable porous medium modeled by the Biot system of poroelasticity. Mass conservation, balance of stress, and the Beavers-Joseph-Saffman condition are imposed on the interface. We consider a fully mixed Biot formulation based on a weakly symmetric stress-displacement-rotation elasticity system and Darcy velocity-pressure flow formulation. A velocity-pressure formulation is used for the Stokes equations. The interface conditions are incorporated through the introduction of the traces of structure velocity and Darcy pressure as Lagrange multipliers. Existence and uniqueness of a solution are established for the continuous weak formulation. Stability and error analysis is performed for the semi-discrete continuous-in-time mixed finite element scheme. Numerical experiments are presented in confirmation of the theoretical results.

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Nonconforming finite element methods for a Stokes/Biot fluid–poroelastic structure interaction model

Cited by 6 publications

References 21 publications

A mixed elasticity formulation for fluid–poroelastic structure interaction

A mixed elasticity formulation for fluid–poroelastic structure interaction

Parameter-robust methods for the Biot-Stokes interfacial coupling without Lagrange multipliers

A mixed elasticity formulation for fluid-poroelastic structure interaction

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