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A posteriori error estimates for adaptive finite element discretizations of boundary control problems. (English) Zbl 1104.65066
The authors consider boundary optimal control problems for a linear second order elliptic boundary value problem with constrained control of the following form: \[ \text{minimize }J(y, u):= {1\over 2}\| y- y^d\|^2_{0,\Omega}+ {\alpha\over 2}\| u- u^d\|^2_{0, \Gamma_1}\text{ over }(y,u)\in H^1_{0,\Gamma_2}(\Omega)\times K \] \[ \text{subject to }-\Delta y+ cy= f\quad\text{in }\Omega,\quad n\cdot\nabla y= u\quad\text{on }\Gamma_1. \] For this problems an a posteriori error analysis of adaptive finite element approximations is considered.
The performance of the adaptive finite element approximation is illustrated by numerical results for selected test problems.

65K10 Numerical optimization and variational techniques
49J20 Existence theories for optimal control problems involving partial differential equations
49M15 Newton-type methods
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