Analysis of Finite Element Methods and Domain Decomposition Algorithms for a Fluid-Solid Interaction Problem

This paper is concerned with the finite element Galerkin approximations for a fluid-solid interaction model proposed in [X. Feng, P. Lee, and Y. Wei, Appl. Anal., submitted]. Both continuous-time and discrete-time approximations are formulated and analyzed. Optimal order a priori estimates for the errors in L^∞(H¹) and L^∞(L²) are derived. The main difficulty for the error estimates is caused by the interface conditions which describe the interaction between a fluid and a solid on their contact surface, and it is overcome by using a boundary duality argument of Douglas and Dupont [Numer. Math., 20 (1973), pp. 213--237] to handle the terms involving the interface conditions. Parallelizable domain decomposition algorithms are also proposed and analyzed for efficiently solving the finite element systems.