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Finite element convergence for the time-dependent Joule heating problem with mixed boundary conditions by Jensen, Max; Målqvist, Axel; Persson, Anna is a scholarly article available to read on EtoBox.

What is Finite element convergence for the time-dependent Joule heating problem with mixed boundary conditions about?

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 the difference in regularity within the domain.

Author

Jensen, Max; Målqvist, Axel; Persson, Anna

Published

2018

Language

EN