Semidiscrete Finite Element Approximations of a Linear Fluid-Structure Interaction Problem

Semidiscrete finite element approximations of a linear fluid-structure interaction problem are studied. First, results concerning a divergence-free weak formulation of the interaction problem are reviewed. Next, semidiscrete finite element approximations are defined, and the existence of finite element solutions is proved with the help of an auxiliary, discretely divergence-free formulation. A discrete inf-sup condition is verified, and the existence of a finite element pressure is established. Strong a priori estimates for the finite element solutions are also derived. Then, by passing to the limit in the finite element approximations, the existence of a strong solution is demonstrated and semidiscrete error estimates are obtained.