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On convergence in elliptic shape optimization. (English) Zbl 1354.49093

Summary: The present paper aims at analyzing the existence and convergence of approximate solutions in shape optimization. Motivated by illustrative examples, an abstract setting of the underlying shape optimization problem is suggested, taking into account the so-called two norm discrepancy. A Ritz – Galerkin-type method is applied to solve the associated necessary condition. Existence and convergence of approximate solutions are proved, provided that the infinite dimensional shape problem admits a stable second order optimizer. The rate of convergence is confirmed by numerical results.

MSC:

49Q10 Optimization of shapes other than minimal surfaces
49K20 Optimality conditions for problems involving partial differential equations
49M15 Newton-type methods
65K10 Numerical optimization and variational techniques
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