An approximation of semiconductor device by mixed finite element method and characteristics-mixed finite element method

被引：16

作者：

Yang, Qing ^{[1
]}

Yuan, Yirang ^{[2
]}

机构：

[1] Shandong Normal Univ, Sch Math Sci, Jinan 250014, Peoples R China

[2] Shandong Univ, Inst Math, Jinan 250100, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2013年 / 225卷

关键词：

Semiconductor device; Mixed finite element method; Characteristics-mixed finite element method; Post-processing step; Error estimates; MISCIBLE DISPLACEMENT; POROUS-MEDIA;

D O I：

10.1016/j.amc.2013.09.067

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The mathematical model of a semiconductor device is described by a system of three quasi-linear partial differential equations for initial boundary value problem. The electric potential is governed by an elliptic equation. The electron and hole concentrations are governed by two equations of convection-dominated diffusion type. Standard mixed finite element is used for the electric potential equation. A characteristics-mixed finite element method is presented for the concentration equations. This scheme conserves mass locally. In order to derive the optimal L2-norm error estimates, a post-processing step is included in the approximation to the scalar concentration. Numerical experiment is presented finally to validate the theoretical analysis. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：407 / 424

页数：18

共 13 条

[1] A CHARACTERISTICS-MIXED FINITE-ELEMENT METHOD FOR ADVECTION-DOMINATED TRANSPORT PROBLEMS [J].

ARBOGAST, T ;

WHEELER, MF .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1995, 32 (02) :404-424

[2]

DOUGLAS J, 1987, MAT APL COMPUT, V6, P25

[3] CONVERGENCE ANALYSIS OF AN APPROXIMATION OF MISCIBLE DISPLACEMENT IN POROUS-MEDIA BY MIXED FINITE-ELEMENTS AND A MODIFIED METHOD OF CHARACTERISTICS [J].

EWING, RE ;

RUSSELL, TF ;

WHEELER, MF .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1984, 47 (1-2) :73-92

[4]

Jerome J.W., 1994, MATH THEORY APPROXIM

[5] MIXED FINITE-ELEMENTS IN IR3 [J].

NEDELEC, JC .

NUMERISCHE MATHEMATIK, 1980, 35 (03) :315-341

[6]

Raviart P.-A., 1977, Lecture Notes in Mathematics, V606, P292, DOI DOI 10.1007/BFB0064470

[7] TIME-STEPPING ALONG CHARACTERISTICS WITH INCOMPLETE ITERATION FOR A GALERKIN APPROXIMATION OF MISCIBLE DISPLACEMENT IN POROUS-MEDIA [J].

RUSSELL, TF .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1985, 22 (05) :970-1013

[8]

Scholz R., 1983, Calcolo, V20, P355, DOI 10.1007/BF02576470

[9] An approximation of incompressible miscible displacement in porous media by mixed finite element method and characteristics-mixed finite element method [J].

Sun, Tongjun ;

Yuan, Yirang .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 228 (01) :391-411

[10]

[杨青 YANG Qing], 2008, [系统科学与数学, Journal of Systems Science and Mathematical Sciences], V28, P725

← 1 2 →