, Volume 53, Issue 2, pp 475-496
Date: 08 Nov 2012

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

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Abstract

We prove strong convergence of conforming finite element approximations to the stationary Joule heating problem with mixed boundary conditions on Lipschitz domains in three spatial dimensions. We show optimal global regularity estimates on creased domains and prove a priori and a posteriori bounds for shape regular meshes.

Communicated by Jan Hesthaven.