Numerical resolution of an exact heat conduction model with a delay term |
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Authors: | Marco Campo Jose R Fernandez and Ramon Quintanilla |
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Institution: | Departamento de Matem\''aticas, ETS de Ingenieros de Caminos, Canales y Puertos, Universidade da Coru\~na, Campus de Elvi\~na, 15071 A Coru\~na, Spain,Departamento de Matem\''atica Aplicada I, Universidade de Vigo, ETSI Telecomunicaci\''on, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain and Departamento de Matem\''aticas, E.S.E.I.A.A.T.-U.P.C., Colom 11, 08222 Terrassa, Barcelona, Spain |
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Abstract: | 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. |
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Keywords: | Thermoelasticity exact heat condution delay parameter finite elements a priori error estimates |
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