Finite element convergence for the time-dependent Joule heating problem with mixed boundary conditions

Jensen, Max, Målqvist, Axel and Persson, Anna (2020) Finite element convergence for the time-dependent Joule heating problem with mixed boundary conditions. IMA Journal of Numerical Analysis. ISSN 0272-4979

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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.

Item Type: Article
Keywords: Joule heating problem, Thermistor, Finite element convergence, Nonsmooth domains, Mixed boundary conditions, Regularity
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
SWORD Depositor: Mx Elements Account
Depositing User: Mx Elements Account
Date Deposited: 04 Sep 2020 08:43
Last Modified: 09 Oct 2020 14:45
URI: http://sro.sussex.ac.uk/id/eprint/93508

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