Optimal [formula omitted] error estimates of stabilizer-free weak Galerkin finite element method for the drift-diffusion problem.

We continue our effort in Li et al. (2024) to develop a stabilizer-free weak Galerkin finite element method (SFWG-FEM) for the two-dimensional unsteady-state drift-diffusion (DD) model. The transient state equation includes both the first derivative convection and the second derivative diffusion terms, and it couples with a Poisson potential equation. The piecewise P k (k ≥ 1) polynomials elements in the interior and on the boundaries are utilized for both electron concentration and electric potential functions. The vector function of [ P j (K) ] 2 (j ≥ j 0) for the discrete weak gradient space is used on each element K. The main difficulty is the treatment of the non-linearity and coupling of the system. Based on an introduced Ritz projection and two L 2 projection operators, optimal error estimates of O (Δ t + h k + 1) in the L 2 norm and O (Δ t + h k) in the energy-like norm are derived. Numerical experiments are presented to illustrate the theoretical analysis. • Optimal estimate of stabilizer-free WG method for drift-diffusion model is derived. • The method is flexible while reducing complexity in analyzing and programming. • A Ritz projection that can be applied to estimate other problems is introduced. [ABSTRACT FROM AUTHOR]