Finite element convergence analysis for the thermoviscoelastic Joule heating problem
Målqvist, Axel and Stillfjord, Tony LU
(2017)
In BIT Numerical Mathematics
57(3).
p.787-810
- 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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2cab0372-9393-4433-a63d-f4c224e37f2d
- author
- Målqvist, Axel
and Stillfjord, Tony
LU
- publishing date
- 2017-03-15
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Convergence analysis, Finite elements, Joule heating, Partial differential equations, Thermistor, Thermoviscoelastic
- in
- BIT Numerical Mathematics
- volume
- 57
- issue
- 3
- pages
- 24 pages
- publisher
- Springer
- external identifiers
-
- scopus:85015234402
- ISSN
- 0006-3835
- DOI
- 10.1007/s10543-017-0653-1
- language
- English
- LU publication?
- no
- additional info
- ).
- id
- 2cab0372-9393-4433-a63d-f4c224e37f2d
- date added to LUP
- 2024-01-23 17:26:25
- date last changed
- 2024-02-23 13:33:30
@article{2cab0372-9393-4433-a63d-f4c224e37f2d,
abstract = {{<p>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.</p>}},
author = {{Målqvist, Axel and Stillfjord, Tony}},
issn = {{0006-3835}},
keywords = {{Convergence analysis; Finite elements; Joule heating; Partial differential equations; Thermistor; Thermoviscoelastic}},
language = {{eng}},
month = {{03}},
number = {{3}},
pages = {{787--810}},
publisher = {{Springer}},
series = {{BIT Numerical Mathematics}},
title = {{Finite element convergence analysis for the thermoviscoelastic Joule heating problem}},
url = {{http://dx.doi.org/10.1007/s10543-017-0653-1}},
doi = {{10.1007/s10543-017-0653-1}},
volume = {{57}},
year = {{2017}},
}