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

Jensen, M.University of Sussex,Univ Sussex, Dept Math, Brighton BN1 9QH, E Sussex, England. (författare)

QC 20220210
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.

Målqvist, Axel,1978Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,University of Gothenburg,Chalmers tekniska högskola,Chalmers University of Technology,Chalmers Univ Technol, Dept Math Sci, SE-41296 Gothenburg, Sweden.;Univ Gothenburg, SE-41296 Gothenburg, Sweden.(Swepub:cth)axel (författare)
Persson, AnnaKTH,Matematisk statistik(Swepub:kth)u1uymzwt (författare)
University of SussexUniv Sussex, Dept Math, Brighton BN1 9QH, E Sussex, England. (creator_code:org_t)

Ingår i:Ima Journal of Numerical Analysis: Oxford University Press (OUP)42:1, s. 199-2280272-49791464-3642

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Av lärosätet: Göteborgs universitet; Chalmers tekniska högskola; Kungliga Tekniska Högskolan

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