TY - JOUR
T1 - On the Linear Thermoelasticity with Two Porosities: Numerical Aspects
AU - Bazarra , Noelia
AU - Fernández , José R.
AU - Leseduarte , Mari Carme
AU - Magaña , Antonio
AU - Quintanilla , Ramón
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 172
EP - 194
PY - 2020
DA - 2020/02
SN - 17
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/13646.html
KW - Thermoelasticity with two porosities, finite elements, a priori error estimates, numerical simulations.
AB - <p style="text-align: justify;">In this work we analyze, from the numerical point of view, a dynamic problem
involving a thermoelastic rod. Two porosities are considered: the first one is the macro-porosity,
connected with the pores of the material, and the other one is the micro-porosity, linked with the
fissures of the skeleton. The mechanical problem is written as a set of hyperbolic and parabolic
partial differential equations. An existence and uniqueness result and an energy decay property
are stated. Then, a fully discrete approximation is introduced using the finite element method
and the backward Euler scheme. A discrete stability property and a priori error estimates are
proved, from which the linear convergence of the algorithm is derived under suitable additional
regularity conditions. Finally, some numerical simulations are presented to show the behaviour of
the approximation.</p>