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arXiv · 1606.00345

Finite element convergence analysis for the thermoviscoelastic Joule heating problem

Axel Målqvist·Tony Stillfjord
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Abstract

We consider a system of equations that model the temperature, electric potential and deformation of a thermoviscoelastic body. A typical application is a thermistor; an electrical component that can be used e.g. as a surge protector, temperature sensor or for very precise positioning. We introduce a full discretization based on standard finite elements in space and a semi-implicit Euler-type method in time. For this method we prove optimal convergence orders, i.e. second-order in space and first-order in time. The theoretical results are verified by several numerical experiments in two and three dimensions.

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Axel Målqvist, Tony Stillfjord. 2016-06-01. Finite element convergence analysis for the thermoviscoelastic Joule heating problem. https://doi.org/10.1007/s10543-017-0653-1

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