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

摘要: 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 discrete-time are formulated analyzed. Optimal order priori estimates errors $L^\infty(H^1)$ $L^\infty(L^2)$ derived. The main difficulty error caused by interface conditions which describe between fluid solid on their contact surface, it overcome using boundary duality argument of Douglas Dupont [Numer. Math., 20 (1973), pp. 213--237] to handle terms involving conditions. Parallelizable domain decomposition algorithms also analyzed efficiently solving systems.