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Finite element convergence for the time-dependent Joule heating problem with mixed boundary conditions
journal contribution
posted on 2023-06-09, 21:30 authored by Max Jensen, Axel Målqvist, Anna PerssonWe 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.
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Publication status
- Published
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- Accepted version
Journal
IMA Journal of Numerical AnalysisISSN
0272-4979Publisher
Oxford University PressExternal DOI
Issue
1Volume
42Page range
199-228Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2020-09-04First Open Access (FOA) Date
2021-10-08First Compliant Deposit (FCD) Date
2020-09-03Usage metrics
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