Numerical solution of a charge transport problem in DG-MOSFET

We propose and describe in detail a new effective numerical algorithm for finding the stationary solutions of charge transport problem in DG-MOSFET transistor. For mathematical description of charge transport process a hydrodynamical MEP model is used. It is worth noting that this model is a set of nonlinear PDE's with small parameters and specific boundary conditions corresponding to DG-MOSFET. It makes the computational process much more complicated. The aim of this work is the construction and the realization of effective numerical algorithm for solving such kind of difficult numerical problems. The proposed algorithm is based on the stabilization method, the application of regularized smoothing operators and ideas of schemes without saturation.