Volume 14, Issue 2
Numerical Analysis of a Thermoelastic Diffusion Problem with Voids

J. R. Fernández & M. Masid

Int. J. Numer. Anal. Mod., 14 (2017), pp. 153-174.

Published online: 2016-05

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  • Abstract

In this paper we consider, from the numerical point of view, a thermoelastic diffusion porous problem. This is written as a coupled system of two hyperbolic equations, for the displacement and porosity fields, and two parabolic equations, for the temperature and chemical potential fields. Its variational formulation leads to a coupled system of four parabolic variational equations in terms of the velocity, porosity speed, temperature and chemical potential. The existence and uniqueness of weak solutions, as well as an energy decay property, are recalled. Then, the numerical approximation is introduced by using the finite element method for the spatial approximation and the implicit Euler scheme to discretize the time derivatives. A stability property is proved and some a priori error estimates are obtained, from which the convergence of the algorithm is derived and, under suitable additional regularity conditions, its linear convergence is deduced. Finally, some numerical approximations are presented to demonstrate the accuracy of the algorithm and to show the behaviour of the solution.

  • Keywords

Thermoelasticity, porosity, diffusion, finite element approximations, error estimates and numerical simulations.

  • AMS Subject Headings

74F05, 74F10, 65M60, 65M15, 65M12, 74K10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-14-153, author = {}, title = {Numerical Analysis of a Thermoelastic Diffusion Problem with Voids}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {14}, number = {2}, pages = {153--174}, abstract = {

In this paper we consider, from the numerical point of view, a thermoelastic diffusion porous problem. This is written as a coupled system of two hyperbolic equations, for the displacement and porosity fields, and two parabolic equations, for the temperature and chemical potential fields. Its variational formulation leads to a coupled system of four parabolic variational equations in terms of the velocity, porosity speed, temperature and chemical potential. The existence and uniqueness of weak solutions, as well as an energy decay property, are recalled. Then, the numerical approximation is introduced by using the finite element method for the spatial approximation and the implicit Euler scheme to discretize the time derivatives. A stability property is proved and some a priori error estimates are obtained, from which the convergence of the algorithm is derived and, under suitable additional regularity conditions, its linear convergence is deduced. Finally, some numerical approximations are presented to demonstrate the accuracy of the algorithm and to show the behaviour of the solution.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/415.html} }
TY - JOUR T1 - Numerical Analysis of a Thermoelastic Diffusion Problem with Voids JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 153 EP - 174 PY - 2016 DA - 2016/05 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/415.html KW - Thermoelasticity, porosity, diffusion, finite element approximations, error estimates and numerical simulations. AB -

In this paper we consider, from the numerical point of view, a thermoelastic diffusion porous problem. This is written as a coupled system of two hyperbolic equations, for the displacement and porosity fields, and two parabolic equations, for the temperature and chemical potential fields. Its variational formulation leads to a coupled system of four parabolic variational equations in terms of the velocity, porosity speed, temperature and chemical potential. The existence and uniqueness of weak solutions, as well as an energy decay property, are recalled. Then, the numerical approximation is introduced by using the finite element method for the spatial approximation and the implicit Euler scheme to discretize the time derivatives. A stability property is proved and some a priori error estimates are obtained, from which the convergence of the algorithm is derived and, under suitable additional regularity conditions, its linear convergence is deduced. Finally, some numerical approximations are presented to demonstrate the accuracy of the algorithm and to show the behaviour of the solution.

J. R. Fernández & M. Masid. (1970). Numerical Analysis of a Thermoelastic Diffusion Problem with Voids. International Journal of Numerical Analysis and Modeling. 14 (2). 153-174. doi:
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