The authors study the spatially semidiscrete piecewise linear finite element method for the nonlinear parabolic problem
in , on , in , where is a bounded domain in , a positive number, and given functions from to , . This parabolic problem describes the temperature profile of a thermistor device with electrical resistivity . The full discrete backward Euler method and the Crank-Nicolson-Galerkin scheme are also considered. An algorithm for solving the fully discrete problem is proposed but no numerical results are presented.