Finite element convergence for the time-dependent Joule heating problem with mixed boundary conditions
Journal article, 2022

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.



nonsmooth domains

Joule heating problem

mixed boundary conditions

finite element convergence


Max Jensen

University of Sussex

Axel Målqvist

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Anna Persson

Royal Institute of Technology (KTH)

IMA Journal of Numerical Analysis

0272-4979 (ISSN) 1464-3642 (eISSN)

Vol. 42 1 199-228

Subject Categories

Computational Mathematics


Mathematical Analysis



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Latest update

2/3/2022 2