Finite element convergence analysis for the thermoviscoelastic Joule heating problem
Artikel i vetenskaplig tidskrift, 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

Thermistor

Thermoviscoelastic

Convergence analysis

Finite elements

Joule heating

Författare

Axel Målqvist

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Göteborgs universitet

Tony Stillfjord

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

BIT (Copenhagen)

0006-3835 (ISSN)

Vol. 57 3 787-810

Ämneskategorier

Matematisk analys

DOI

10.1007/s10543-017-0653-1

Mer information

Skapat

2017-10-11