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A monolithic mixed finite element method for a fluid-structure interaction problem

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  • Bean, Maranda
  • Yi, Son-Young

Abstract

We propose a numerical method for modeling the interaction of a Stokes fluid and a linear elastic solid. The model problem is expressed in the stress-displacement formulation for the linear elastodynamics in the solid region and the stress-velocity formulation for the Stokes equations in the fluid region. These two systems are coupled in such a way that the interface conditions are imposed naturally in the resulting weak formulation, which is based on the Hellinger–Reissner variational principle. For the time discretization, we use a three-level scheme for each time step, with an exception at the first time step. We provide a priori error analysis for fully-discrete, nonconforming mixed finite element methods and show some numerical results to confirm our theoretical results.

Suggested Citation

  • Bean, Maranda & Yi, Son-Young, 2019. "A monolithic mixed finite element method for a fluid-structure interaction problem," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    • Handle: RePEc:eee:apmaco:v:363:y:2019:i:c:10
    DOI: 10.1016/j.amc.2019.124615
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    1. Unknown, 2008. "Recommendations Of The European Project," Economics of Agriculture, Institute of Agricultural Economics, vol. 55(1).
    2. Anonymous, 2008. "The UNESCO Parsi Zoroastrian Project," Working Papers id:1517, eSocialSciences.
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