In this work, the quasistatic thermoviscoelastic thermistor problem is considered. The thermistor model describes the combination of the effects due to the heat, electrical current conduction and Joule's heat generation. The variational formulation leads to a coupled system of nonlinear variational equations for which the existence of a weak solution is recalled. Then, a fully discrete algorithm is introduced based on the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived and, under suitable regularity assumptions, the linear convergence of the scheme is deduced. Finally, some numerical simulations are performed in order to show the behaviour of the algorithm.
Mots clés : thermoviscoelastic thermistor, error estimates, finite elements, numerical simulations
@article{M2AN_2006__40_2_353_0,
author = {Fern\'andez, Jos\'e R.},
title = {Numerical analysis of the quasistatic thermoviscoelastic thermistor problem},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {353--366},
publisher = {EDP-Sciences},
volume = {40},
number = {2},
year = {2006},
doi = {10.1051/m2an:2006016},
mrnumber = {2241827},
zbl = {1108.74013},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2006016/}
}
TY - JOUR AU - Fernández, José R. TI - Numerical analysis of the quasistatic thermoviscoelastic thermistor problem JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2006 SP - 353 EP - 366 VL - 40 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2006016/ DO - 10.1051/m2an:2006016 LA - en ID - M2AN_2006__40_2_353_0 ER -
%0 Journal Article %A Fernández, José R. %T Numerical analysis of the quasistatic thermoviscoelastic thermistor problem %J ESAIM: Modélisation mathématique et analyse numérique %D 2006 %P 353-366 %V 40 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2006016/ %R 10.1051/m2an:2006016 %G en %F M2AN_2006__40_2_353_0
Fernández, José R. Numerical analysis of the quasistatic thermoviscoelastic thermistor problem. ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 2, pp. 353-366. doi : 10.1051/m2an:2006016. http://www.numdam.org/articles/10.1051/m2an:2006016/
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