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A posteriori error estimates for control problems governed by Stokes equations. (English) Zbl 1028.49025

Summary: We derive a posteriori error estimates for the finite element approximation of distributed optimal control problems governed by the Stokes equations. We obtain a posteriori error estimators for both the state and the control approximation in the \(L^{2}\) norm and the \(H^{1}\) norm. These estimates can be used to construct reliable adaptive finite element approximation for the control problems.

MSC:

49M25 Discrete approximations in optimal control
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q30 Navier-Stokes equations
49M15 Newton-type methods
49J20 Existence theories for optimal control problems involving partial differential equations
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