A conforming exponentially fitted finite element scheme for the semiconductor continuity equations in 3D

The paper presents an exponentially fitted tetrahedral Finite element method for the decoupled continuity equations in the drift-diffusion model of semiconductor devices. This finite element method is based on a set of piecewise exponential basis functions constructed on a tetrahedral mesh. Error estimates for the approximate solution and its associated flux are given, where the error bounds depend on some first-order seminorms of the exact solution, the exact flux and the coefficient function of the convection terms.