Numerical resolution of an exact heat conduction model with a delay term
| Autor: | Ramón Quintanilla, M. Campo, José R. Fernández |
|---|---|
| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. GRAA - Grup de Recerca en Anàlisi Aplicada |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
a priori error estimates
74 Mechanics of deformable solids::74F Coupling of solid mechanics with other effects [Classificació AMS] Discretization General Mathematics 74 Mechanics of deformable solids::74K Thin bodies structures [Classificació AMS] Matemàtiques i estadística::Matemàtica aplicada a les ciències [Àrees temàtiques de la UPC] 02 engineering and technology exact heat condution 01 natural sciences Calor -- Transmissió -- Models matemàtics Thermoelastic damping Heat --Transmission -- Mathematical models 0203 mechanical engineering 35 Partial differential equations::35G General higher-order equations and systems [Classificació AMS] Applied mathematics Uniqueness 0101 mathematics Thermoelasticity Mathematics 65 Numerical analysis::65M Partial differential equations initial value and time-dependent initial-boundary value problems [Classificació AMS] Partial differential equation delay parameter Thermal conduction Backward Euler method Finite element method 010101 applied mathematics 020303 mechanical engineering & transports Rate of convergence finite elements 37 Dynamical systems and ergodic theory::37N Applications [Classificació AMS] Termoelasticitat |
| Zdroj: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) Recercat. Dipósit de la Recerca de Catalunya instname |
| Popis: | In this paper we analyze, from the numerical point of view, a dynamic thermoelastic problem. Here, the so-called exact heat conduction model with a delay term is used to obtain the heat evolution. Thus, the thermomechanical problem is written as a coupled system of partial differential equations, and its variational formulation leads to a system written in terms of the velocity and the temperature fields. An existence and uniqueness result is recalled. Then, fully discrete approximations are introduced by using the classical finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A priori error estimates are proved, from which the linear convergence of the algorithm could be derived under suitable additional regularity conditions. Finally, a two-dimensional numerical example is solved to show the accuracy of the approximation and the decay of the discrete energy. |
| Databáze: | OpenAIRE |
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