|Table of Contents|

Characteristic finite element method for 2-D nonlinear convection-diffusion problems(PDF)

长安大学学报（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

Issue:
2010年03期
Page:
105-110
Research Field:
Publishing date:
2010-06-20

Info

Title:
Characteristic finite element method for 2-D nonlinear convection-diffusion problems
Author(s):
ZHANG Yin-di;  FENG Jian-hu;  YU Jian-sheng
School of Science, Chang'an University, Xi'an 710064, Shaanxi, China
Keywords:
convection-diffusion equation;  characteristic finite element method;  error estimate;  convection-dominated;  Sobolev spaces
PACS:
O241.82
DOI:
-
Abstract:
Applying characteristic finite element Galerkin method, a numerical solution was discussed for 2-D nonlinear convection-dominated diffusion problems. A characteristic finite element Galerkin scheme was established for 2-D nonlinear convection-dominated diffusion equation here. Two optimal error estimates of the scheme were given. The estimates analysis and numerical test show that, for 2-D nonlinear convection-dominated diffusion problems, the scheme here has the better convergence and stability than others, and avoids the oscillating with finite element or finite difference procedure. 2 tabs, 6 figs, 10 refs.

References:

[1] Douglas J J,Russell T F.Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures[J].SIAM J Numer Anal,1982,19(5):871-885.
[2]Russell T F.Time stepping along characteristics with incomplete iteration for a Galerkin approximation of miscible displacement in porous media [J].SIAM J Numer Anal,1985,22(5):970-1030.
[3]Dawson C N,Russell T.Wheeler M F.Some improved error estimates for the modified method of characteristics[J].SIAM J Numer Anal,1989,26(6):1487-1512.
[4]袁益让.在多孔介质中完全可压缩可混溶驱动问题的差分方法[J].计算数学,1993,15(1):16-28. YUAN Yi-rang.Finite difference methods for a compressible miscible displacement problem in porous media[J].Mathematica Numerica Sinica,1993,15(1):16-28.
[5]CHEN Z X.Relationships among characteristic finite element methods for advection diffusion problems[J].Journal of the Korean SIAM,2002(6):1-15.
[6]CHEN Z X.Characteristic mixed discontinuous finite element methods for advection dominated diffusion problems[J].Computer Methods in Applied Mechanics and Engineering,2002,191(23/24):2509-2538.
[7]张引娣,李开泰.非线性对流扩散方程特征有限元法的误差估计[J].长安大学学报:自然科学版,2004,24(6):106-110. ZHANG Yin-di,LI Kai-tai.The error estimates of the characteristic finite element method for nonlinear advection-diffusion equation[J].Journal of Chang'an University:Natural Science Edition,2004,24(6):106-110.
[8]李开泰,马逸尘.数理方程Hilbert空间方法[M].西安:西安交通大学出版社,1992.
[9]李开泰,黄庆怀.有限元方法及其应用[M].西安:西安交通大学出版社,1992.
[10]揣锦华,李军民.C++程序设计语言[M].西安:西安电子科技大学出版社,2003.

Memo

Memo:
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Last Update: 2010-06-20