Numerical Analysis of Nonstationary Thermistor Problem

Abstract

The thermistor problem is coupled system of nonlinear PDEs which consists of the heat equation with the Joule heating as a source, and the current conservation equation with temperature dependent electrical conductivity. In this paper we make a numerical analysis of the nonsteady thermistor problem. $L^∞(Ω), W^{1,∞}(Ω)$ stability and error bounds for a piecewise linear finite element approximation are given.