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arXiv · 1808.03584

Shape differentiability of Lagrangians and application to Stokes problem

V. A. Kovtunenko·K. Ohtsuka
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Abstract

A class of convex constrained minimization problems over polyhedral cones for geometry-dependent quadratic objective functions is considered in a functional analysis framework. Shape differentiability of the primal minimization problem needs a bijective property for mapping of the primal cone. This restrictive assumption is relaxed to bijection of the dual cone within the Lagrangian formulation as a primal-dual minimax problem. In this paper, we give results on primal-dual shape sensitivity analysis that extends the class of shape-differentiable problems supported by explicit formula of the shape derivative. We apply the results to the Stokes problem under mixed Dirichlet-Neumann boundary conditions subject to the divergence-free constraint.

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V. A. Kovtunenko, K. Ohtsuka. 2018-08-10. Shape differentiability of Lagrangians and application to Stokes problem. https://doi.org/10.1137/17m1125327

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