Functional a posteriori Error Estimates for Time-periodic Parabolic Optimal Control Problems
Langer, U., Repin, S., & Wolfmayr, M. (2016). Functional a posteriori Error Estimates for Time-periodic Parabolic Optimal Control Problems. Numerical Functional Analysis and Optimization, 37 (10), 1267-1294. doi:10.1080/01630563.2016.1200077
Published inNumerical Functional Analysis and Optimization
© 2016 Taylor & Francis. This is a final draft version of an article whose final and definitive form has been published by Taylor & Francis. Published in this repository with the kind permission of the publisher.
This article 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 the 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.