Year: 2020
Author: Noelia Bazarra, José R. Fernández, Mari Carme Leseduarte, Antonio Magaña, Ramón Quintanilla
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 2 : pp. 172–194
Abstract
In this work we analyze, from the numerical point of view, a dynamic problem involving a thermoelastic rod. Two porosities are considered: the first one is the macro-porosity, connected with the pores of the material, and the other one is the micro-porosity, linked with the fissures of the skeleton. The mechanical problem is written as a set of hyperbolic and parabolic partial differential equations. An existence and uniqueness result and an energy decay property are stated. Then, a fully discrete approximation is introduced using the finite element method and the backward Euler scheme. A discrete stability property and a priori error estimates are proved, from which the linear convergence of the algorithm is derived under suitable additional regularity conditions. Finally, some numerical simulations are presented to show the behaviour of the approximation.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2020-IJNAM-13646
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 2 : pp. 172–194
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Thermoelasticity with two porosities finite elements a priori error estimates numerical simulations.