Functional A Posteriori Error Estimates for Time-Periodic Parabolic Optimal Control Problems. (2nd October 2016)

• Record Type: Journal Article
• Authors: Langer, Ulrich; Repin, Sergey; Wolfmayr, Monika
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 10(2016)
• Page Start: 1267
• Page End: 1294
• Publication Date: 2016-10-02
• Subjects: Functional a posteriori error estimates -- multiharmonic finite element methods -- parabolic time-periodic optimal control problems; 35Kxx -- 65M60 -- 65M70 -- 65M15 -- 65K10; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1200077
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: 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.