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A fully discrete scheme for the pressure–stress formulation of the time-domain fluid–structure interaction problem

  • Carlos García
  • Gabriel N. Gatica
  • Antonio Márquez
  • Salim Meddahi
Article

Abstract

We propose an implicit Newmark method for the time integration of the pressure–stress formulation of a fluid–structure interaction problem. The space Galerkin discretization is based on the Arnold–Falk–Winther mixed finite element method with weak symmetry in the solid and the usual Lagrange finite element method in the acoustic medium. We prove that the resulting fully discrete scheme is well-posed and uniformly stable with respect to the discretization parameters and Poisson ratio, and we provide asymptotic error estimates. Finally, we present numerical tests to confirm the asymptotic error estimates predicted by the theory.

Keywords

Mixed finite elements Fluid–solid interaction Error estimates 

Mathematics Subject Classification

65N30 65M12 65M15 74H15 

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Copyright information

© Springer-Verlag Italia S.r.l. 2017

Authors and Affiliations

  • Carlos García
    • 1
  • Gabriel N. Gatica
    • 1
  • Antonio Márquez
    • 2
  • Salim Meddahi
    • 3
  1. 1.CI²MA and Departamento de Ingeniería MatemáticaUniversidad de ConcepciónConcepciónChile
  2. 2.Departamento de Construcción e Ingeniería de FabricaciónUniversidad de OviedoOviedoSpain
  3. 3.Departamento de Matemáticas, Facultad de CienciasUniversidad de OviedoOviedoSpain

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