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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.

##### MSC:
 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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