TY - JOUR
T1 - Numerical Analysis of a Thermoelastic Diffusion Problem with Voids
AU - J. R. Fernández & M. Masid
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 - <p style="text-align: justify;">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.</p>