Open AccessOn existence and numerical approximation in phase-lag thermoelasticity with two temperatures
Author(s) -
M. Campo,
M. I. M. Copetti,
José R. Fernández,
R. Quintanilla
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021130
Subject(s) - thermoelastic damping , uniqueness , discretization , mathematics , backward euler method , mathematical analysis , phase lag , stability (learning theory) , finite element method , relaxation (psychology) , work (physics) , numerical analysis , lag , physics , thermal , thermodynamics , computer science , psychology , social psychology , computer network , machine learning
In this work we study from both variational and numerical points of view a thermoelastic problem which appears in the dual-phase-lag theory with two temperatures. An existence and uniqueness result is proved in the general case of different Taylor approximations for the heat flux and the inductive temperature. Then, in order to provide the numerical analysis, we restrict ourselves to the case of second-order approximations of the heat flux and first-order approximations for the inductive temperature. First, variational formulation of the corresponding problem is derived and an energy decay property is proved. Then, a fully discrete scheme is introduced by using the finite element method for the approximation of the spatial variable and the implicit Euler scheme for the discretization of the time derivatives. A discrete stability