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Russian Journal of Numerical Analysis and Mathematical Modelling

Editor-in-Chief: Dymnikov, Valentin P. / Kuznetsov, Yuri

Managing Editor: Vassilevski, Yuri V.

Editorial Board: Agoshkov, Valeri I. / Amosov, Andrey A. / Kaporin, Igor E. / Kobelkov, Georgy M. / Mikhailov, Gennady A. / Repin, Sergey I. / Shaidurov, Vladimir V. / Shokin, Yuri I. / Tyrtyshnikov, Eugene E.

IMPACT FACTOR 2018: 0.779

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Volume 32, Issue 4


A posteriori estimates for a coupled piezoelectric model

Ulrich Langer
  • Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences Altenberger Str. 69, 4040 Linz, Austria
  • Other articles by this author:
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/ Sergey Repin
  • Corresponding author
  • St. Petersburg Department of V. A. Steklov Institute of Mathematics, St. Petersburg 191024 Russia
  • Peter the Great St. Petersburg Polytechnic University, St. Petersburg 195251, Russia
  • University of Jyväskulä, Jyväskulä, PO Box 35, FI-40014, Finland
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/ Tatiana Samrowski
  • School of Engineering, Zurich University of Applied Sciences, Technikumstrasse 9, CH-8401 Winterthur, Switzerland
  • Other articles by this author:
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Published Online: 2017-07-26 | DOI: https://doi.org/10.1515/rnam-2017-0025


The paper is related to a coupled problem describing piezoelectric effects in an elastic body. For this problem, we deduce majorants of the distance between the exact solution and any approximation in the respective energy class of functions satisfying the boundary conditions. The majorants are fully computable and do not contain mesh dependent constants. They vanish if and only if an approximate solution coincides with the exact one and provide guaranteed upper bounds of errors in terms of the natural energy norm associated with the coupled problem studied.

Keywords: Coupled systems of partial differential equations; piezoelectricity problem; a posteriori error estimates

MSC 2010: 35J20; 65N15; 65N30


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About the article

Received: 2017-04-27

Accepted: 2017-06-07

Published Online: 2017-07-26

Published in Print: 2017-08-28

Citation Information: Russian Journal of Numerical Analysis and Mathematical Modelling, Volume 32, Issue 4, Pages 259–266, ISSN (Online) 1569-3988, ISSN (Print) 0927-6467, DOI: https://doi.org/10.1515/rnam-2017-0025.

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