一维非稳态半导体漂移扩散模型的弱Galerkin有限元法

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.该格式在单元内部用分片k(k≥0)次多项式来逼近静电势Ψ和电子浓度n,用分片k+1次多项式来逼近静电势Ψ和电子浓度n的导数.本文得到了半离散问题的最优误差估计.数值实验验证了理论结果.

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

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 of degree $ k(k\geq 0) $ for the electrostatic potential $ \psi $ and electron concentration $ n $ approximations in the interior of elements, and piecewise polynomials of degree $ k+1 $ for the weak derivative of electrostatic potential $ \psi $ and electron concentration $ n $. Optimal error estimates are derived for the semi-discrete problem and numerical experiments are provided to verify our theoretical results.