A Posteriori Error Analysis for a New Fully Mixed Isotropic Discretization of the Stationary Stokes-Darcy Coupled Problem

Houédanou, Koffi Wilfrid; Adetola, Jamal; Allaoui, Mohamed

doi:10.1155/2020/8628739

Cited by 3 publications

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References 43 publications

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“…3.3 (i.e., identity (65) and Equation ( 72)) and some a inverse estimates of Lemma 7 (Cf. [37] for details).…”

Section: Lemma 10 ([7]mentioning

confidence: 99%

A Posteriori Error Analysis for a Lagrange Multiplier Method for a Stokes/Biot Fluid-Poroelastic Structure Interaction Model

Houédanou

2021

Abstract and Applied Analysis

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In this work, we develop an a posteriori error analysis of a conforming mixed finite element method for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic medium on isotropic meshes in ℝ d , d ∈ 2 , 3 . The approach utilizes a Lagrange multiplier method to impose weakly the interface conditions [Ilona Ambartsumyan et al., Numerische Mathematik, 140 (2): 513-553, 2018]. The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient. The proof of reliability makes use of suitable auxiliary problems, diverse continuous inf-sup conditions satisfied by the bilinear forms involved, Helmholtz decomposition, and local approximation properties of the Clément interpolant. On the other hand, inverse inequalities and the localization technique based on simplexe-bubble and face-bubble functions are the main tools for proving the efficiency of the estimator. Up to minor modifications, our analysis can be extended to other finite element subspaces yielding a stable Galerkin scheme.

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“…3.3 (i.e., identity (65) and Equation ( 72)) and some a inverse estimates of Lemma 7 (Cf. [37] for details).…”

Section: Lemma 10 ([7]mentioning

confidence: 99%

A Posteriori Error Analysis for a Lagrange Multiplier Method for a Stokes/Biot Fluid-Poroelastic Structure Interaction Model

Houédanou

2021

Abstract and Applied Analysis

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Uncoupling evolutionary groundwater-surface water flows: stabilized mixed methods in both porous media and fluid regions

2022

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Error Estimation of Euler Method for the Instationary Stokes–Biot Coupled Problem

Houédanou

Adetola

2021

Journal of Mathematics

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In this paper, we study a finite element computational model for solving the interaction between a fluid and a poroelastic structure that couples the Stokes equations with the Biot system. Equilibrium and kinematic conditions are imposed on the interface. A mixed Darcy formulation is employed, resulting in continuity of flux condition of essential type. A Lagrange multiplier method is used to impose weakly this condition. With the obtained finite element solutions, the error estimators are performed for the fully discrete formulations.

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A Posteriori Error Analysis for a New Fully Mixed Isotropic Discretization of the Stationary Stokes-Darcy Coupled Problem

Abstract: In this paper, we develop an a posteriori error analysis for the stationary Stokes-Darcy coupled problem approximated by conforming the finite element method on isotropic meshes in ℝ d , … Show more

Cited by 3 publications

References 43 publications

A Posteriori Error Analysis for a Lagrange Multiplier Method for a Stokes/Biot Fluid-Poroelastic Structure Interaction Model

A Posteriori Error Analysis for a Lagrange Multiplier Method for a Stokes/Biot Fluid-Poroelastic Structure Interaction Model

Uncoupling evolutionary groundwater-surface water flows: stabilized mixed methods in both porous media and fluid regions

Error Estimation of Euler Method for the Instationary Stokes–Biot Coupled Problem

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