A Fully Discrete Ultra-Weak Discontinuous Galerkin Method for Solving the Drift-Diffusion Model of Semiconductor Devices

Abstract

In this paper, we study an ultra-weak discontinuous Galerkin (UWDG) method for spatial discretization to solve the drift-diffusion (DD) model of one-dimensional semiconductor devices. Optimal error estimates are obtained using a special projection for both the semi-discrete and fully discrete UWDG schemes with smooth solutions. In the fully discrete UWDG scheme, we use an explicit third-order total variation diminishing Runge-Kutta method, which ensures stability under general temporal-spatial conditions. Numerical simulations are also performed to verify the analysis.