The mathematical model of a semiconductor device is governed by a system of quasi-linear partial differential equations. The electric potential equation is approximated by a mixed finite element method, and the concentration equations are approximated by a standard Galerkin method. We estimate the error of the numerical solutions in the sense of the Lq norm. To linearize the full discrete scheme of the problem, we present an efficient two-grid method based on the idea of Newton iteration. The main procedures are to solve the small scaled nonlin...
