Finite Element Convergence for the Joule Heating Problem with Mixed Boundary Conditions

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.

arXiv commentKeywords: Joule heating problem, thermistors, a posteriori error analysis, a priori error analysis, finite element method

Cited by in corpus (1)

• Finite element convergence analysis for the thermoviscoelastic Joule heating problem