CONVERGENCE ANALYSIS OF FINITE ELEMENT APPROXIMATIONS OF THE JOULE HEATING PROBLEM IN THREE SPATIAL DIMENSIONS

Abstract. 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 extensive numerical examples in three spatial dimensions. The first example demonstrates the convergence of the method and the second example shows an engineering application