Volume 40, Number 2, March-April 2006
|Page(s)||353 - 366|
|Published online||21 June 2006|
Numerical analysis of the quasistatic thermoviscoelastic thermistor problem
Departamento de Matemática Aplicada,
Facultade de Matemáticas, Campus Sur s/n, Universidade de Santiago de Compostela,
15782 Santiago de Compostela, Spain. firstname.lastname@example.org
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.
Mathematics Subject Classification: 65N15 / 65N30 / 74D10 / 74S05 / 74S20
Key words: Thermoviscoelastic thermistor / error estimates / finite elements / numerical simulations.
© EDP Sciences, SMAI, 2006
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.