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Interface control domain decomposition (ICDD) methods for the Stokes problem
journal contributionposted on 11.09.2015 by Marco Discacciati, Paola Gervasio, Alfio Quarteroni
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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.
- Mathematical Sciences