Convergence analysis of finite element approximations of the Joule heating problem in three spatial dimensions
Michael Holst, Mats G. Larson, Axel Målqvist, Robert Söderlund · BIT Numerical Mathematics · 2010
In this paper we present a finite element discretization of the Joule-heating problem. We prove existence of solution to the discrete formulation and strong convergence of the finite element solution to the weak solution, up to a sub-sequence. We also present numerical examples in three spatial dimensions. The first example demonstrates the convergence of the method in the second example we consider an engineering application.