Shape Hessian for generalized Oseen flow by differentiability of a minimax: A Lagrangian approach. (English) Zbl 1174.76008
Summary: The goal of this paper is to compute the shape Hessian for a generalized Oseen problem with nonhomogeneous Dirichlet boundary condition by the velocity method. The incompressibility will be treated by penalty approach. The structure of the shape gradient and shape Hessian with respect to the shape of the variable domain for a given cost functional are established by an application of the Lagrangian method with function space embedding technique.
MSC:
| 76D55 | Flow control and optimization for incompressible viscous fluids |
| 49Q12 | Sensitivity analysis for optimization problems on manifolds |
| 49K35 | Optimality conditions for minimax problems |
| 76D07 | Stokes and related (Oseen, etc.) flows |
Keywords:
shape sensitivity analysis; shape Hessian; Eulerian semiderivative; differentiability of a minimax; Oseen flowReferences:
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