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Delfour, M.C. and Zolésio, J.-P. (2001) Shapes and Geometries: Analysis, Differential Calculus, and Optimization. SIAM, Philadelphia.

has been cited by the following article:

• TITLE: A Numerical Method for Shape Optimal Design in the Oseen Flow with Heat Transfer

  AUTHORS: Wenjing Yan, Axia Wang, Guoxing Guan

  KEYWORDS: Shape Optimization, Oseen Equations, Shape Gradient, Minimax Principle, Convective Heat Transfer, Function Space Parametrization Technique

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.3 No.10, October 29, 2015

  ABSTRACT: This paper is concerned with the optimal design of an obstacle located in the viscous and incompressible fluid which is driven by the steady-state Oseen equations with thermal effects. The structure of shape gradient of the cost functional is derived by applying the differentiability of a minimax formulation involving a Lagrange functional with a space parametrization technique. A gradient type algorithm is employed to the shape optimization problem. Numerical examples indicate that our theory is useful for practical purpose and the proposed algorithm is feasible.