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

Maranda Bean and Son-Young Yi

Applied Mathematics and Computation, 2019, vol. 363, issue C, -

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.

Keywords: Fluid-structure interaction; Mixed finite element method; Hellinger–Reissner principle (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:363:y:2019:i:c:10

DOI: 10.1016/j.amc.2019.124615

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