Functional a posteriori error estimates for time-periodic parabolic optimal control problems
Provides rigorous error bounds for a class of optimal control problems, benefiting researchers in numerical analysis and computational optimal control.
The paper derives functional a posteriori error estimates for multiharmonic finite element approximations of time-periodic parabolic optimal control problems, providing guaranteed upper bounds for state, co-state, and cost functional errors, confirmed by numerical tests showing high efficiency.
This paper is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of functional type, which are easily computable and provide guaranteed upper bounds for the state and co-state errors as well as for the cost functional. These theoretical results are confirmed by several numerical tests that show high efficiency of the a posteriori error bounds.