A B-spline finite element method for the thermistor problem with the modified electrical conductivity

摘要

In this paper, approximate steady-state solutions of a one-dimensional positive temperature coefficient thermistor problem with a modified step function electrical conductivity are obtained by using the Galerkin cubic B-spline finite element method. It is shown that the computational results obtained by the method display the correct physical characteristics of the problem, and they are found to be in very good agreement with the exact solution. It is also shown that the numerical solution exhibits the expected convergence to the exact one as the mesh size is refined. Further a Fourier stability analysis of the method is investigated.