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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.
}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/613.html} }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.