For the transient behavior of a semiconductor device, the modified
method of characteristics finite element alternating-direction procedures with
moving meshes are put forward. Some techniques, such as calculus of variations,
operator-splitting, characteristic method, generalized L^2 projection, energy
method, negative norm estimate and prior estimates and techniques are
employed. Optimal order estimates in L^2 norm are derived for the error in the
approximation solution. Thus the well-known theoretical problem has been
thoroughly and completely solved.