RT Journal Article
T1 A MGT thermoelastic problem with two relaxation parameters
A1 Bazarra Garcia, Noelia
A1 Fernández García, José Ramón
A1 Quintanilla, Ramón
K1 1206 Análisis Numérico
AB In this paper, we consider, from both analytical and numerical viewpoints, a thermoelastic problem. The so-called MGT model, with two different relaxation parameters, is used for both the displacements and the thermal displacement, leading to a linear coupled system made by two third-order in time partial differential equations. Then, using the theory of linear semi-groups the existence and uniqueness to this problem is proved. If we restrict ourselves to the one-dimensional case, the exponential decay of the energy is obtained assuming some conditions on the constitutive parameters. Then, using the classical finite element method and the implicit Euler scheme, we introduce a fully discrete approximation of a variational formulation of the thermomechanical problem. A main a priori error estimates result is shown, from which we conclude the linear convergence under suitable additional regularity conditions. Finally, we present some one-dimensional numerical simulations to demonstrate the convergence of the fully discrete approximation, the behavior of the discrete energy decay and the dependence on a coupling parameter.
PB Zeitschrift für angewandte Mathematik und Physik
SN 00442275
YR 2023
FD 2023-09-15
LK http://hdl.handle.net/11093/5279
UL http://hdl.handle.net/11093/5279
LA eng
NO Zeitschrift für angewandte Mathematik und Physik, 74(5): 197-1-197-20 (2023)
NO Agencia Estatal de Investigación | Ref. PID2019-105118GB-I00
DS Investigo
RD 05-dic-2024