Finite element approaches to the PTC thermistor problem

In this paper, subdomain collocation (SC) and Petrov-Galerkin (PG) methods based on spline finite elements have been applied to the one-dimensional positive temperature coefficient (PTC) thermistor problem with a temperature dependent ramp function electrical conductivity to obtain the predicted temperature distributions and the locations of the free boundaries in the steady-state case. The numerical results obtained by the present methods have been compared with the exact solution and also those obtained by earlier authors. A Fourier stability analysis of each method is investigated.