Analysis of a Poro-Thermo-Viscoelastic Model of Type III
Noelia Bazarra,
José A. López-Campos,
Marcos López,
Abraham Segade,
José R. Fernández
Affiliations
Noelia Bazarra
Departamento de Matemática Aplicada I, Universidade de Vigo, ETSI Telecomunicación, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain
José A. López-Campos
Departamento de Ingeniería Mecánica, Máquinas y Motores Térmicos y Fluídos, Escola de Enxeñaría Industrial, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain
Marcos López
Departamento de Ingeniería Mecánica, Máquinas y Motores Térmicos y Fluídos, Escola de Enxeñaría Industrial, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain
Abraham Segade
Departamento de Ingeniería Mecánica, Máquinas y Motores Térmicos y Fluídos, Escola de Enxeñaría Industrial, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain
José R. Fernández
Departamento de Matemática Aplicada I, Universidade de Vigo, ETSI Telecomunicación, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain
In this work, we numerically study a thermo-mechanical problem arising in poro-viscoelasticity with the type III thermal law. The thermomechanical model leads to a linear system of three coupled hyperbolic partial differential equations, and its weak formulation as three coupled parabolic linear variational equations. Then, using the finite element method and the implicit Euler scheme, for the spatial approximation and the discretization of the time derivatives, respectively, a fully discrete algorithm is introduced. A priori error estimates are proved, and the linear convergence is obtained under some suitable regularity conditions. Finally, some numerical results, involving one- and two-dimensional examples, are described, showing the accuracy of the algorithm and the dependence of the solution with respect to some constitutive parameters.
