Finite element approaches to the PTC thermistor problem (Q1774926)

This paper deals with the study of an initial boundary value problem of coupled nonlinear partial differential equations consisting of a heat-flow equation with the joule heating as a source and a current flow equation with a temperature dependent electrical conductivity. The authors apply the subdomain collocation and Petrov-Galerkin methods to obtain approximate steady-state solutions. These numerical results are compared with the exact solutions obtained in previous works. A Fourier stability analysis of each method is also carried out in the present paper.