This paper proposes a weak Galerkin (WG) finite element method for solving time dependent drift-diffusion problems in one dimension. This drift-diffusion model involves a Poisson equation for the electrostatic potential coupled to a nonlinear convection diffusion equation for the electron concentration. The weak Galerkin method adopts piecewise polynomials for the electrostatic potential and electron concentration approximations in the interior of elements, and piecewise polynomials for the weak derivative of electrostatic potential and electron concentration. Optimal error estimates are derived for the semi-discrete problem and numerical experiments are provided to verify our theoretical results.
