2018/11/23 by Gang Chen, Chen, Gang, Peter Monk +3
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1811.09705
openalex publication_date 2018/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We propose a hybridizable discontinuous Galerkin (HDG) finite element method to approximate the solution of the time dependent drift-diffusion problem. This system involves a nonlinear convection diffusion equation for the electron concentration u coupled to a linear Poisson problem for the the electric potential ϕ. The non-linearity in this system is the product of the ∇ ϕ with u. An improper choice of a numerical scheme can reduce the convergence rate. To obtain optimal HDG error estimates for ϕ, u and their gradients, we utilize two different HDG schemes to discretize the nonlinear convection diffusion equation and the Poisson equation. We prove optimal order error estimates for the semidiscrete problem. We also present numerical experiments to support our theoretical results.