An a priori error analysis of a Lord–Shulman poro-thermoelastic problem with microtemperatures

In this paper, we deal with the numerical analysis of the Lord–Shulman thermoelastic problem with porosity and microtemperatures. The thermomechanical problem leads to a coupled system composed of linear hyperbolic partial differential equations written in terms of transformations of the displacemen...

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Veröffentlicht in:Acta mechanica Jg. 231; H. 10; S. 4055 - 4076
Hauptverfasser: Baldonedo, Jacobo, Bazarra, Noelia, Fernández, José R., Quintanilla, Ramón
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Vienna Springer Vienna 01.10.2020
Springer
Springer Nature B.V
Schlagworte:
Analysis
Approximation
Classical and Continuum Physics
Computer simulation
Control
Differential equations
Dynamical Systems
Engineering
Engineering Fluid Dynamics
Engineering Thermodynamics
Error analysis
Finite element method
Heat and Mass Transfer
Mathematical analysis
Numerical analysis
Original Paper
Partial differential equations
Porosity
Solid Mechanics
Stability analysis
Theoretical and Applied Mechanics
Vibration
ISSN:0001-5970, 1619-6937
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:In this paper, we deal with the numerical analysis of the Lord–Shulman thermoelastic problem with porosity and microtemperatures. The thermomechanical problem leads to a coupled system composed of linear hyperbolic partial differential equations written in terms of transformations of the displacement field and the volume fraction, the temperature and the microtemperatures. An existence and uniqueness result is stated. Then, a fully discrete approximation is introduced using the finite element method and the implicit Euler scheme. A discrete stability property is shown, and an a priori error analysis is provided, from which the linear convergence is derived under suitable regularity conditions. Finally, some numerical simulations are presented to demonstrate the accuracy of the approximation, the comparison with the classical Fourier theory and the behavior of the solution in two-dimensional examples.
Bibliographie:ObjectType-Article-1
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ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-020-02738-z