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

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. (C) 2019 Elsevier Inc. All rights reserved.