The Characteristic Finite Element Alternating-Direction Method with Moving Meshes for the Transient Behavior of a Semiconductor Device

Abstract

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.