Structure-preserving finite difference schemes for a semilinear thermoelastic system with second order time derivative
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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.
KeywordsFinite difference method Discrete variational derivative method Semilinear thermoelastic system Error estimate
Mathematics Subject Classification65M06 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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