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.


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