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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Vydáno v:Acta mechanica Ročník 231; číslo 10; s. 4055 - 4076
Hlavní autoři: Baldonedo, Jacobo, Bazarra, Noelia, Fernández, José R., Quintanilla, Ramón
Médium: Journal Article
Jazyk:angličtina
Vydáno: Vienna Springer Vienna 01.10.2020
Springer
Springer Nature B.V
Témata:
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
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Popis
Shrnutí: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.
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ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-020-02738-z