Error Estimates for a Finite Element Method for the Drift-diffusion Semiconductor Device Equations

In this paper, optimal error estimates are obtained for a method for numerically solving the so-called unipolar model (a one-dimensional simpliied version of the drift-diiusion semiconductor device equations). The numerical method combines a mixed nite element method using a continuous piecewise-linear approximation of the electric eld with an explicit upwinding nite element method using a piecewise-constant approximation of the electron concentration. For initial and boundary data ensuring that the electron concentration is smooth, the L 1 (L 1)-error for the electron concentration and the L 1 (L 1)-error of the electric eld are both proven to be of order x. The error analysis is carried out rst in the zero diiusion case in detail and then extended to the full unipolar model.