Convergence of a fluid–structure interaction problem decoupled by a Neumann control over a single time step

• Published in: Journal of mathematical analysis and applications Vol. 437; no. 1; pp. 645 - 667
• Main Authors: Kuberry, Paul, Lee, Hyesuk
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01-05-2016
• Subjects: Finite element method; Fluid–structure interaction; Optimal control; Finite element method; Fluid–structure interaction; Optimal control
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2016.01.022

Building off of previous analytical results for recasting fluid–structure interaction into an optimal control setting, an a priori error estimate is given for the optimality system by means of BRR theory. The convergence of the steepest descent method is proven in a discrete setting for a sufficiently small time step and mesh size. A numerical study is included supporting the theoretical rate of convergence over a single time step. Additional results demonstrate optimal convergence in space and time over several time steps.