TY - JOUR
T1 - An Approximation of Three-Dimensional Semiconductor Devices by Mixed Finite Element Method and Characteristics-Mixed Finite Element Method
AU - Qing Yang & Yirang Yuan
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 356
EP - 382
PY - 2015
DA - 2015/08
SN - 8
DO - http://doi.org/10.4208/nmtma.2015.my12031
UR - https://global-sci.org/intro/article_detail/nmtma/12414.html
KW - 
AB - <p style="text-align: justify;">The mathematical model for semiconductor devices in three space dimensions are numerically discretized. The system consists of three quasi-linear partial differential equations about three physical variables: the electrostatic potential, the electron concentration and the hole concentration. We use standard mixed finite element method to approximate the elliptic electrostatic potential equation. For the two convection-dominated concentration equations, a characteristics-mixed finite element method is presented. The scheme is locally conservative. The optimal $L^2$-norm error estimates are derived by the aid of a post-processing step. Finally, numerical experiments are presented to validate the theoretical analysis.</p>