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A posteriori error estimates of recovery type for distributed convex optimal control problems. (English) Zbl 1128.65048

Summary: In this paper, the authors derive a posteriori error estimates of recovery type, and present the superconvergence analysis for the finite element approximation of distributed convex optimal control problems. They provide a posteriori error estimates of recovery type for both the control and the state approximation, which are generally equivalent. Under some stronger assumptions, they are further shown to be asymptotically exact. Such estimates, which are apparently not available in the literature, can be used to construct adaptive finite element approximation schemes and as a reliability bound for the control problems. Numerical results illustrating the theoretical results are presented.

MSC:

65K10 Numerical optimization and variational techniques
49K99 Optimality conditions
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