Japan Journal of Industrial and Applied Mathematics

, Volume 35, Issue 3, pp 1213–1244 | Cite as

Structure-preserving finite difference schemes for a semilinear thermoelastic system with second order time derivative

  • Keisuke Yano
  • Shuji YoshikawaEmail author
Original Paper Area 2


In this article we study a semilinear thermoelastic system which consists of heat equation and beam equation with second-order time derivative. Although in Yoshikawa (ZAMM 95(12):1393–1410, 2015; IMA J Numer Anal 37:477–504, 2017) the second author proposed the structure-preserving finite difference scheme for the system transformed to first order system with respect to time variable, here we propose structure-preserving finite difference schemes for the original system with second-order time derivative. The main purpose of this article is to give mathematical analysis for the scheme such as existence of solution and error estimate.


Finite difference method Discrete variational derivative method Semilinear thermoelastic system Error estimate 

Mathematics Subject Classification

65M06 74S20 



This work was partially supported by JSPS KAKENHI Grant-in-Aid for Scientific Research(C), Grant no. 16K05234. Authors express their deep gratitude to Mr. Shimura and anonymous referees for their kind advices.


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Copyright information

© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Engineering for Production and Environment, Graduate School of Science and EngineeringEhime UniversityMatsuyamaJapan
  2. 2.Division of Mathematical Sciences, Faculty of Science and TechnologyOita UniversityOitaJapan

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