一维非稳态半导体漂移扩散模型的弱Galerkin有限元法

A weak Galerkin finite element method for 1D drift-diffusion model of time-dependent semiconductor devices

摘要:

本文提出了一种求解一维非稳态半导体漂移扩散模型的弱Galerkin有限元法.该模型是一个描述静电势分布的泊松方程和一个刻画电子守恒性的非线性对流扩散方程的耦合系统.在弱Galerkin格式中,本文在单元内部用分片多项式来逼近静电势和电子浓度,以及静电势和电子浓度的弱导数，进而得到了半离散问题的最优误差估计.数值试验验证了理论结果.

Abstract:

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.