Analysis of finite element methods and domain decomposition algorithms fora 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 approximati ons are formulated and analyzed. Optimal order a priori estimates for the e rrors in L-infinity (H-1) and L-infinity (L-2) are derived. The main diffic ulty for the error estimates is caused by the interface conditions which de scribe 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 Du pont [Numer. Math., 20 (1973), pp. 213-237] to handle the terms involving t he interface conditions. Parallelizable domain decomposition algorithms are also proposed and analyzed for efficiently solving the finite element syst ems.