Finite element convergence analysis for the thermoviscoelastic Joule heating problem
Journal article, 2017

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.

Partial differential equations



Convergence analysis

Finite elements

Joule heating


Axel Målqvist

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Tony Stillfjord

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

BIT (Copenhagen)

0006-3835 (ISSN)

Vol. 57 787-810

Subject Categories

Mathematical Analysis