# Numerical analysis of the quasistatic thermoviscoelastic thermistor problem

ESAIM: Mathematical Modelling and Numerical Analysis (2006)

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

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topFernández, 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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