# Numerical analysis of the quasistatic thermoviscoelastic thermistor problem

• Volume: 40, Issue: 2, page 353-366
• ISSN: 0764-583X

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## Abstract

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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.

## How to cite

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Fernández, José R.. "Numerical analysis of the quasistatic thermoviscoelastic thermistor problem." ESAIM: Mathematical Modelling and Numerical Analysis 40.2 (2006): 353-366. <http://eudml.org/doc/249716>.

@article{Fernández2006,
abstract = { 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. },
author = {Fernández, José R.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Thermoviscoelastic thermistor; error estimates; finite elements; numerical simulations.; variational formulation; existence; weak solution; finite element method},
language = {eng},
month = {6},
number = {2},
pages = {353-366},
publisher = {EDP Sciences},
title = {Numerical analysis of the quasistatic thermoviscoelastic thermistor problem},
url = {http://eudml.org/doc/249716},
volume = {40},
year = {2006},
}

TY - JOUR
AU - Fernández, José R.
TI - Numerical analysis of the quasistatic thermoviscoelastic thermistor problem
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2006/6//
PB - EDP Sciences
VL - 40
IS - 2
SP - 353
EP - 366
AB - 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.
LA - eng
KW - Thermoviscoelastic thermistor; error estimates; finite elements; numerical simulations.; variational formulation; existence; weak solution; finite element method
UR - http://eudml.org/doc/249716
ER -

## References

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