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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| Vydáno v: | Mathematical methods in the applied sciences Ročník 43; číslo 5; s. 2759 - 2771 |
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30.03.2020
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| ISSN: | 0170-4214, 1099-1476 |
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| Abstract | 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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| AbstractList | 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. 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. Peer Reviewed |
| Author | Fernández, José R. Bazarra, Noelia Magaña, Antonio Quintanilla, Ramón |
| Author_xml | – sequence: 1 givenname: Noelia surname: Bazarra fullname: Bazarra, Noelia organization: Universidade de Vigo – sequence: 2 givenname: José R. orcidid: 0000-0002-8533-1858 surname: Fernández fullname: Fernández, José R. email: jose.fernandez@uvigo.es organization: Universidade de Vigo – sequence: 3 givenname: Antonio orcidid: 0000-0003-0879-0759 surname: Magaña fullname: Magaña, Antonio organization: Universitat Politécnica de Catalunya – sequence: 4 givenname: Ramón orcidid: 0000-0001-7059-7058 surname: Quintanilla fullname: Quintanilla, Ramón organization: Universitat Politécnica de Catalunya |
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| Cites_doi | 10.1007/BF01177123 10.1080/01495739208946136 10.1080/01495730701738272 10.1115/1.2822329 10.1080/01495739.2013.839619 10.1016/j.aml.2009.03.010 10.1016/0017-9310(95)00052-B 10.1007/s00028-018-0457-z 10.1007/BF00044969 10.1016/j.mechrescom.2009.05.002 10.1098/rspa.1995.0020 10.1016/j.cma.2006.05.006 |
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| Snippet | 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... 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... |
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| SubjectTerms | 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 |
| Title | Numerical analysis of a dual‐phase‐lag model involving two temperatures |
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