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On optimal shape design of systems governed by mixed Dirichlet-Signorini boundary value problems. (English) Zbl 0603.49020

The authors consider the problem of finding an optimal shape for systems governed by the mixed unilateral boundary value problem of Dirichlet- Signorini type. The corresponding state problem is approximated by a penalty method and the resulting approximated design problem is discretized by means of the finite element method. The convergence of the solutions of the discretized problems to a solution of the original problem is demonstrated. Moreover, the discretized versions are formulated as a nonlinear programming problem and numerical results are given and compared with the results of two other methods.
Reviewer: P.Quittner

MSC:

49M15 Newton-type methods
35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)
49M30 Other numerical methods in calculus of variations (MSC2010)
49J40 Variational inequalities
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65K10 Numerical optimization and variational techniques
74P99 Optimization problems in solid mechanics
93C20 Control/observation systems governed by partial differential equations
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