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Shape reconstruction of an inverse Stokes problem. (English) Zbl 1138.76031

Summary: This paper deals with the shape reconstruction of a viscous incompressible flow governed by Stokes equations. For the approximate solution of ill-posed and nonlinear problem, we propose a regularized Newton method. A theoretical foundation of Newton method is given by establishing the differentiability of the initial-boundary value problem with respect to interior boundary curve in the sense of a domain derivative. Numerical examples show that our theory is useful for practical purpose, and that the proposed algorithm is feasible.

MSC:

76D07 Stokes and related (Oseen, etc.) flows
76M25 Other numerical methods (fluid mechanics) (MSC2010)
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