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Finite element convergence analysis for the thermoviscoelastic Joule heating problem

Målqvist, Axel and Stillfjord, Tony LU orcid (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.

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author
and
publishing date
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
2025-10-14 12:24:37
@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}},
}