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ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Numerical analysis of the quasistatic thermoviscoelastic thermistor problem
José R. Fernández
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 40 / Issue 2 / March 2006

Published online by Cambridge University Press:

21 June 2006, pp. 353-366

Print publication:

March 2006
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In this work, the quasistatic thermoviscoelastic thermistor problem isconsidered. The thermistor model describes the combination of the effects due tothe heat, electrical current conduction and Joule's heat generation. The variationalformulation leads to a coupled system of nonlinear variational equations for whichthe existence of a weak solution is recalled.Then, a fully discrete algorithm is introduced based on the finite elementmethod to approximate the spatial variable and an Euler scheme to discretizethe time derivatives. Error estimates are derived and, under suitableregularity assumptions, the linear convergence of the scheme is deduced.Finally, some numerical simulations are performed in order to show the behaviourof the algorithm.