Frequency-explicit asymptotic error estimates for a stress-pressure formulation of a time harmonic fluid-solid interaction problem

Abstract

This paper deals with a mixed finite element method to solve the interior solid–fluid interaction problem in harmonic regime. The main variables of our formulation are the stress tensor in the solid and the pressure in the fluid domain. The problem is shown to be well-posed and the continuous functional calculus theorem is used to obtain wavenumber-explicit stability estimates. We discretize the problem by using the mixed finite element method of Arnold–Falk–Winther in the solid and the classical Lagrange finite element in the fluid. We obtain quasi-optimal error estimates under a suitable restriction on the mesh size. Finally, our analysis is illustrated with some numerical experiments.