DISCACCIATI, M., GERVASIO, P. and QUARTERONI, A., 2013. Interface control domain decomposition (ICDD) methods for the Stokes problem. Journal of Coupled Systems and Multiscale Dynamics, 1 (3), pp. 372 - 392
We study the Interface Control Domain Decomposition (ICDD) for the Stokes equation. We reformulate this
problem introducing auxiliary control variables that represent either the traces of the fluid velocity or the normal
stress across subdomain interfaces. Then, we characterize suitable cost functionals whose minimization permits
to recover the solution of the original problem. We analyze the well-posedness of the optimal control problems
associated to the different choices of the cost functionals, and we propose a discretization of the problem based
on hp finite elements. The effectiveness of the proposed methods is illustrated through several numerical tests.
The first author acknowledges funding from the European
Union Seventh Framework Programme (FP7/2007-
2013) under grant agreement n◦ 294229.