A porous thermoelastic problem with microtemperatures

In this article, we consider from the numerical point of view a thermodynamical problem involving a linear elastic material with inner structure, whose particles in addition to the classical displacement possess microtemperatures. The variational formulation of this problem is written as a system of...

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Bibliographic Details
Published inJournal of thermal stresses Vol. 40; no. 2; pp. 145 - 166
Main Authors Fernández, J. R., Masid, M.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 01.02.2017
Taylor & Francis Ltd
Subjects
Approximation
Computer simulation
Convergence
Displacement
Error estimates
Finite element analysis
finite elements
Materials elasticity
Mathematical analysis
Mathematical models
microtemperatures
numerical simulations
Porosity
Regularity
Temperature
Thermodynamics
thermoporoelasticity
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Summary:In this article, we consider from the numerical point of view a thermodynamical problem involving a linear elastic material with inner structure, whose particles in addition to the classical displacement possess microtemperatures. The variational formulation of this problem is written as a system of coupled linear parabolic variational equations in terms of velocity, porosity speed, microtemperatures, and temperature. Then, fully discrete approximations are introduced using the finite element method and the backward Euler scheme. A stability property is proved and some a priori error estimates are obtained, from which the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, numerical simulations are presented to demonstrate the accuracy of the approximations and the behavior of the solution.
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content type line 23
ISSN:0149-5739
1521-074X
DOI:10.1080/01495739.2016.1249038