ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis ISBN 978-3-7001-8258-0 Online Edition Research Article
Noelia Bazarra,
José R. Fernández,
Ramón Quintanilla
S. 405 - 420 doi:10.1553/etna_vol60s405 Verlag der Österreichischen Akademie der Wissenschaften doi:10.1553/etna_vol60s405
Abstract: In this paper we study a one-dimensional dynamic thermoelastic problem assuming that the elastic coefficient is negative. Following the ideas proposed by Eringen in the 80s, a nonlocal term is introduced into the constitutive equation for the displacements, leading to a hyperbolic problem. Then, we consider the numerical approximation of the problem by using the classical finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A discrete stability property is proved, and an a priori error analysis is done, from which we can conclude the linear convergence of the approximations under suitable regularity for the continuous solution. Finally, some numerical simulations are presented, including the demonstration of the numerical convergence and the behavior of the discrete energy for several choices of the constitutive parameters. Keywords: nonlocal thermoelasticity, finite elements, discrete stability, a priori error estimates, numerical simulations Published Online: 2024/08/23 08:22:52 Object Identifier: 0xc1aa5572 0x003f4a9f Rights: . Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613. …
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |