A Mixed Method for the Mixed Initial Boundary Value Problems of Equations of Semiconductor Devices - Zhu, Jiang; Wu, Hongwei; Wang, Yuanming (SIAM journal on numerical analysis, 1994)
In this article, the approximation of nonstationary equations of the semiconductor device with mixed boundary conditions is considered. The approximate procedure of this system using a Galerkin method that makes use of a mixed finite element method for the potential equation combined with a finite element method for the concentration equations is presented. Due to the poor regularity properties of the solutions to the semiconductor equations caused by mixed boundary conditions, a nonstandard analysis for the semidiscrete Galerkin procedure is used. Existence and uniqueness of the approximate solution is proved. A convergence analysis is also given for the method.