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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

IMPACT FACTOR 2017: 0.658

CiteScore 2017: 1.05

SCImago Journal Rank (SJR) 2017: 1.291
Source Normalized Impact per Paper (SNIP) 2017: 0.893

Mathematical Citation Quotient (MCQ) 2017: 0.76

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Volume 15, Issue 3


Functional A Posteriori Error Estimates for Parabolic Time-Periodic Boundary Value Problems

Ulrich Langer / Sergey Repin
  • V. A. Steklov Institute of Mathematics in St. Petersburg, Fontanka 27, 191023, St. Petersburg, Russia; and University of Jyväskylä, Finland
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/ Monika Wolfmayr
Published Online: 2015-05-20 | DOI: https://doi.org/10.1515/cmam-2015-0012


The paper is concerned with parabolic time-periodic boundary value problems which are of theoretical interest and arise in different practical applications. The multiharmonic finite element method is well adapted to this class of parabolic problems. We study properties of multiharmonic approximations and derive guaranteed and fully computable bounds of approximation errors. For this purpose, we use the functional a posteriori error estimation techniques earlier introduced by S. Repin. Numerical tests confirm the efficiency of the a posteriori error bounds derived.

Keywords: Parabolic Time-Periodic Boundary Value Problems; Multiharmonic Finite Element Methods; Functional A Posteriori Error Estimates

MSC: 35Kxx; 65M60; 65M70; 65M15

The authors would like to thank the anonymous referees for carefully reading our manuscript and for their valuable comments leading to a substantial improvement of the paper.

About the article

Received: 2014-11-10

Revised: 2015-03-31

Accepted: 2015-04-28

Published Online: 2015-05-20

Published in Print: 2015-07-01

Funding Source: Austrian Academy of Sciences

Funding Source: Austrian Science Fund (FWF)

Award identifier / Grant number: W1214-N15, project DK4

Funding Source: Upper Austrian Government

Award identifier / Grant number: Innovatives OÖ 2010 plus

Citation Information: Computational Methods in Applied Mathematics, Volume 15, Issue 3, Pages 353–372, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2015-0012.

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