Jensen, Max;
Målqvist, Axel;
Persson, Anna;
(2022)
Finite element convergence for the time-dependent Joule heating problem with mixed boundary conditions.
IMA Journal of Numerical Analysis
, 42
(1)
pp. 199-228.
10.1093/imanum/draa068.
Preview |
Text
jouleheating.pdf - Accepted Version Download (472kB) | Preview |
Abstract
Abstract We prove strong convergence for a large class of finite element methods for the time-dependent Joule heating problem in three spatial dimensions with mixed boundary conditions on Lipschitz domains. We consider conforming subspaces for the spatial discretization and the backward Euler scheme for the temporal discretization. Furthermore, we prove uniqueness and higher regularity of the solution on creased domains and additional regularity in the interior of the domain. Due to a variational formulation with a cut-off functional, the convergence analysis does not require a discrete maximum principle, permitting approximation spaces suitable for adaptive mesh refinement, responding to the difference in regularity within the domain.
| Type: | Article |
|---|---|
| Title: | Finite element convergence for the time-dependent Joule heating problem with mixed boundary conditions |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/imanum/draa068 |
| Publisher version: | https://doi.org/10.1093/imanum/draa068 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions. |
| Keywords: | Joule heating problem, Thermistor, Finite element convergence, Nonsmooth domains, Mixed boundary conditions, Regularity |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10156973 |
Archive Staff Only
 |
View Item |
