  We analyze the spatially semidiscrete piecewise linear finite element method
for a nonlocal parabolic equation resulting from thermistor problem. Our
approach is based on the properties of the elliptic projection defined by the
bilinear form associated with the variational formulation of the finite element
method. We assume minimal regularity of the exact solution that yields optimal
order error estimate. The full discrete backward Euler method and the
Crank-Nicolson-Galerkin scheme are also considered. Finally, a simple algorithm
for solving the fully discrete problem is proposed.
