Numerical analysis of a dual‐phase‐lag model involving two temperatures

In this paper, we numerically analyse a phase‐lag model with two temperatures which arises in the heat conduction theory. The model is written as a linear partial differential equation of third order in time. The variational formulation, written in terms of the thermal acceleration, leads to a linea...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences Vol. 43; no. 5; pp. 2759 - 2771
Main Authors: Bazarra, Noelia, Fernández, José R., Magaña, Antonio, Quintanilla, Ramón
Format: Journal Article Publication
Language:English
Published: Freiburg Wiley Subscription Services, Inc 30.03.2020
Subjects:
65 Numerical analysis
65M Partial differential equations, initial value and time-dependent initial-boundary value problems
74 Mechanics of deformable solids
74F Coupling of solid mechanics with other effects
74K Thin bodies, structures
A priori estimates
Acceleration
Approximation
Calor
Classificació AMS
Computer simulation
Conduction heating
Conductive heat transfer
Elements finits, Mètode dels
Finite element method
Finite elements
Heat
Heat conduction
Matemàtica aplicada a les ciències
Matemàtiques i estadística
Mathematical analysis
Mathematical models
Mètodes de simulació
Numerical analysis
Numerical simulations
Partial differential equations
Phase-lag with two temperatures
Simulation methods
Transmission
Transmissió
Àrees temàtiques de la UPC
ISSN:0170-4214, 1099-1476
Online Access:Get full text
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Summary:In this paper, we numerically analyse a phase‐lag model with two temperatures which arises in the heat conduction theory. The model is written as a linear partial differential equation of third order in time. The variational formulation, written in terms of the thermal acceleration, leads to a linear variational equation, for which we recall an existence and uniqueness result and an energy decay property. Then, using the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives, fully discrete approximations are introduced. A discrete stability property is proved, and a priori error estimates are obtained, from which the linear convergence of the approximation is derived. Finally, some one‐dimensional numerical simulations are described to demonstrate the accuracy of the approximation and the behaviour of the solution.
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content type line 14
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.6082