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. https://doi.org/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.
PublisherTaylor & Francis Inc.
Publication in research information system
MetadataShow full item record
Showing items with similar title or keywords.
Wolfmayr, Monika (Elsevier, 2020)In this paper, a new technique is shown for deriving computable, guaranteed lower bounds of functional type (minorants) for two different cost functionals subject to a parabolic time-periodic boundary value problem. Together ...
Tai, Xue-Cheng; Neittaanmäki, Pekka (Wiley, 1991)An efficient method for solving parabolic systems is presented. The proposed method is based on the splitting‐up principle in which the problem is reduced to a series of independent 1D problems. This enables it to be used ...
Kurz, Stefan; Pauly, Dirk; Praetorius, Dirk; Repin, Sergey; Sebastian, Daniel (Springer, 2021)Functional error estimates are well-established tools for a posteriori error estimation and related adaptive mesh-refinement for the finite element method (FEM). The present work proposes a first functional error estimate ...
Langer, Ulrich; Matculevich, Svetlana; Repin, Sergey (Springer International Publishing, 2018)The paper is concerned with reliable space-time IgA schemes for parabolic initial-boundary value problems. We deduce a posteriori error estimates and investigate their applicability to space-time IgA approximations. ...
Neittaanmäki, Pekka; Stachurski, Andrzej (Springer, 1992)In this paper we present a new approach to solve a two-level optimization problem arising from an approximation by means of the finite element method of optimal control problems governed by unilateral boundary-value problems. ...