A multipoint stress-flux mixed finite element method for the Stokes-Biot model

Caucao, Sergio; Li, Tongtong; Yotov, Ivan

doi:10.1007/s00211-022-01310-2

Cited by 13 publications

(1 citation statement)

References 55 publications

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“…Other formulations of this system of equations have also been studied. These include the velocity-pressure (for Stokes) and stress-displacement-velocity-pressure (for poroelasticity) formulation [38] and the stress-velocity-pressure (for Stokes) and stress-displacement-velocity-pressure (for poroelasticity) formulation [17]. A conforming finite element method using Nitsche's technique for the Stokes/Biot problem is studied in [30].…”

Section: Introductionmentioning

confidence: 99%

A hybridizable discontinuous Galerkin method for the coupled Navier–Stokes and Darcy problem

Çeşmelioǧlu

Rhebergen

2023

Journal of Computational and Applied Mathematics

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Section: Introductionmentioning

confidence: 99%

A hybridizable discontinuous Galerkin method for the coupled Navier–Stokes and Darcy problem

Çeşmelioǧlu

Rhebergen

2023

Journal of Computational and Applied Mathematics

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Weak and strong solutions for a fluid‐poroelastic‐structure interaction via a semigroup approach

Avalos,

Gurvich,

Webster

2024

Math Methods in App Sciences

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A filtration system comprising a Biot poroelastic solid coupled to an incompressible Stokes free‐flow is considered in 3D. Across the flat 2D interface, the Beavers‐Joseph‐Saffman coupling conditions are taken. In the inertial, linear, and non‐degenerate case, the hyperbolic‐parabolic coupled problem is posed through a dynamics operator on a chosen energy space, adapted from Stokes‐Lamé coupled dynamics. A semigroup approach is utilized to circumvent issues associated to mismatched trace regularities at the interface. The generation of a strongly continuous semigroup for the dynamics operator is obtained via a non‐standard maximality argument. The latter employs a mixed‐variational formulation in order to invoke the Babuška‐Brezzi theorem. The Lumer‐Philips theorem then yields semigroup generation, and thereby, strong and generalized solutions are obtained. For the linear dynamics, density obtains the existence of weak solutions; we extend to the case where the Biot compressibility of constituents degenerates. Thus, for the inertial linear Biot‐Stokes filtration system, we provide a clear elucidation of strong solutions and a construction of weak solutions, as well as their regularity through associated estimates.

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Mixed Finite Element Methods for the Navier–Stokes–Biot Model

Caucao,

Dalal,

et al. 2024

Lecture Notes in Computer Science

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A multipoint stress-flux mixed finite element method for the Stokes-Biot model

Cited by 13 publications

References 55 publications

A hybridizable discontinuous Galerkin method for the coupled Navier–Stokes and Darcy problem

A hybridizable discontinuous Galerkin method for the coupled Navier–Stokes and Darcy problem

Weak and strong solutions for a fluid‐poroelastic‐structure interaction via a semigroup approach

Mixed Finite Element Methods for the Navier–Stokes–Biot Model

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