On Convergence in Elliptic Shape Optimization | Zendy

Karsten Eppler | Zendy; Helmut Harbrecht | Zendy; Reinhold Schneider | Zendy

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On Convergence in Elliptic Shape Optimization

Author(s) -

Karsten Eppler,

Helmut Harbrecht,

Reinhold Schneider

Publication year - 2007

Publication title -

siam journal on control and optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.486

H-Index - 116

eISSN - 1095-7138

pISSN - 0363-0129

DOI - 10.1137/05062679x

Subject(s) - mathematics , convergence (economics) , norm (philosophy) , shape optimization , rate of convergence , compact convergence , galerkin method , optimization problem , normal convergence , convergence tests , modes of convergence (annotated index) , mathematical optimization , finite element method , pure mathematics , computer science , key (lock) , economics , physics , computer security , political science , law , thermodynamics , economic growth , topological vector space , topological space , isolated point

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.

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