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Numerische Mathematik

, Volume 140, Issue 2, pp 513–553 | Cite as

A Lagrange multiplier method for a Stokes–Biot fluid–poroelastic structure interaction model

  • Ilona Ambartsumyan
  • Eldar Khattatov
  • Ivan Yotov
  • Paolo Zunino
Article
  • 143 Downloads

Abstract

We study a finite element computational model for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic medium. The free fluid is governed by the Stokes equations, while the flow in the poroelastic medium is modeled using the Biot poroelasticity 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 employed to impose weakly this condition. A stability and error analysis is performed for the semi-discrete continuous-in-time and the fully discrete formulations. A series of numerical experiments is presented to confirm the theoretical convergence rates and to study the applicability of the method to modeling physical phenomena and the robustness of the model with respect to its parameters.

Mathematics Subject Classification

76S05 76D07 74F10 65M60 65M12 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Ilona Ambartsumyan
    • 1
  • Eldar Khattatov
    • 1
  • Ivan Yotov
    • 1
  • Paolo Zunino
    • 2
    • 3
  1. 1.Department of MathematicsUniversity of PittsburghPittsburghUSA
  2. 2.Department of Mechanical Engineering and Materials ScienceUniversity of PittsburghPittsburghUSA
  3. 3.MOX, Department of MathematicsPolitecnico di MilanoMilanItaly

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