Numerical analysis of a thermoelastic dielectric problem arising in the Moore–Gibson–Thompson theory
DATE:
2022-11
UNIVERSAL IDENTIFIER: http://hdl.handle.net/11093/4104
EDITED VERSION: https://linkinghub.elsevier.com/retrieve/pii/S0377042722002151
DOCUMENT TYPE: article
ABSTRACT
In this paper, we numerically study a thermoelastic problem arising in the Moore–
Gibson–Thompson theory. Dielectrics effects are also included within the model. The
corresponding problem is written in terms of the displacement field, the temperature
and the electric potential. A viscous term is added in the heat equation to provide
the numerical analysis of the corresponding variational problem. Then, by using the
finite element method and the implicit Euler scheme fully discrete approximations
are introduced. A discrete stability property and a priori error estimates are obtained.
Finally, one- and two-dimensional numerical simulations are shown to demonstrate the
accuracy of the approximation and the behavior of the solution