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非线性对流扩散方程的特征有限元方法和分析 被引量：3

CHARACTERISTIC FINITE ELEMENT METHODS AND ANALYSIS FOR CONVECTION-DIFFUSION EQUATION
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摘要 讨论了非线性对流扩散方程的特征有限元方法及理论分析,应用先验估计理论得出了最优阶误差估计. A characteristic finite element method is introduced and analysis for approximating the solution of threedimensional Convectiondiffusion equation,Optimal order L2 error estimates are demonstrated.
作者 王桂霞
机构地区 内蒙古师范大学数学系
出处 《内蒙古师范大学学报（自然科学汉文版）》 CAS 2003年第2期114-117,共4页 Journal of Inner Mongolia Normal University(Natural Science Edition)
基金 内蒙古师范大学青年基金重点项目(QNZ00112)
关键词 非线性对流扩散方程 特征有限元方法 先验估计 最优阶误差估计 数值解 characteristic finite element Convection-diffusion Optimal error estimates
分类号 O175.29 [理学—基础数学] O241.82 [理学—计算数学]
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参考文献6

  • 1利翁斯J L 郭柏灵 汪礼仍译.非线性边值问题的一些解法[M].广州:中山大学出版社,1992..
  • 2Douglas Jr J, Russell T F. Numerical methods for Convection-dominated diffusion Problem Based on Combining the Method of Characteristics with Finite Element or Finite Difference Procedures [J]. SIAM. J. Number. Anal. ,1982,19(5) :871 - 885.
  • 3Russell T F. Time stepping along characteristic with incomplete iteration for a Galerlin approximation of miscible displacement in porous media [J]. SIAM. J. Number. Anal. ,1985,22(5) :970-1013.
  • 4Ciarlet P G. The Finite Element Method for Elliptic problem [M]. Amsterdam:North- Holland,1978.
  • 5Wheeler M F. A priori error estimates for Galerlin approximation to parabolic differential equation [J]. SIAM. J. Number. Anal. ,1973,10 (5) :723 -759.
  • 6Ewing R E,Wheeler M F. Convergence analysis of an approximation of miscible displacement in porous media by mixedfinite dements and a modified method of characteristics [J]. Computer Methods In Applied Mechanics And Engineering,1984,47 (3) .73 - 92.

同被引文献14

  • 1杨素香,姜子文.一类半线性反应对流扩散模型的特征有限元法[J].科学技术与工程,2005,5(7):393-397. 被引量：3
  • 2袁益让.三维动边值问题的特征混合元方法和分析[J].中国科学（A辑）,1996,26(1):11-22. 被引量：14
  • 3J.Jr.Douglas,T.F.Russell.Numerical methods for convection dominated diffusion problems based on combining the method ofcharacteristics with finite elelement or finite difference procedures[J].SIAM J.Numer.Anal.,1982,19(5):871-885.
  • 4C.N.Dowson,T.F.Russell and M.F.Wheeler.Some improved error estimate for the modified method of characteristics[J].SI-AM J.Numer.Anal.,1989,26:1487-1512.
  • 5R.E.Ewing,T.F.Russell and M.F.Wheeler.Convergence analysis of an approximation of miscible displacement in porousmedia by mixed finite elements and a modified method of characteristics[J].Comput.Methods.Appl.Mech.Engrg.1984,47:73-79.
  • 6陆瑶.二维非线性对流扩散方程的特征有限元分析.数学、力学、物理学、高新技术研究进展,2008,12:357-365.
  • 7Douglas Jr 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.
  • 8Wheeler M F.A priori L2 error estimates for Galerkin approximations to parabolic partial differential equations[J].SIAM J Numer Anal,1973,10(4):723-759.
  • 9J.Jr.Douglas,T.F.Russell.Numerical methods for convection dominated diffusion problems based on combining the methodof characteristics with finite elelement or finite difference procedures[J].SIAM J.Numer.Anal.1982,19(5):871-885.
  • 10R.E.Ewing,T.F.Russell and M.F.Wheeler.Simulation of miscible displacement using mixed finite elements and a modifiedmethod of characteristics[J].7th SPE symposium on reservoir simulation,San Francisco,Nov.1983.

引证文献3

二级引证文献4

内蒙古师范大学学报（自然科学汉文版）
2003年 第2期

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