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A posteriori error estimates of mixed methods for parabolic optimal control problems. (English) Zbl 1219.49025
Summary: We give a brief review on the fully discrete mixed finite element method for general optimal control problems governed by parabolic equations. The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant elements. Furthermore, we derive a-posteriori error estimates for the finite element approximation solutions of optimal control problems. Some numerical examples are given to demonstrate our theoretical results.

MSC:
49M25 Discrete approximations in optimal control
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
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