期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

奇异摄动问题在Bakhvalov-Shishkin网格上的流线扩散有限元逼近 被引量：2

A STREAMLINE-DIFFUSION FINITE ELEMENT APPROXIMATION ON BAKHVALOV-SHISHKIN MESH FOR SINGULARLY PERTURBED PROBLEM
原文传递
导出
摘要 本文采用线性插值的流线扩散有限元在Bakhvalov-Shishkin网格上求解一维对流扩散型的奇异摄动问题.在ε≤N^(-1)的前提下,可以得到,关于扰动参数ε是一致收敛的.在离散的SD范数下,其u-u_I的误差阶提高到N^(-2),u-u_h的误差阶达到N^(-2)(ln N)^(0.5).最后,通过数值算例,验证了理论分析. In this paper, a linear Streamline-Diffusion finite element method on Bakhvalov-Shishkin mesh for singulurly perturbed convectiou - diffusion problem is analyzed. The method is shown to be convergent uniformly in the perturbation parameter 6 provided only that ε≤ N-1. A rate O（N-2（InN）0.5） in a discrete SD norm is established under certain regularity assumptions. Finally, through numerical experiments, we verified the theoretical results.
作者 尹云辉 祝鹏 杨宇博
机构地区 嘉兴学院数理与信息工程学院 嘉兴学院南湖学院
出处 《计算数学》 CSCD 北大核心 2013年第4期365-376,共12页 Mathematica Numerica Sinica
基金 浙江省自然科学基金(LQ12A01014) 嘉兴学院科研启动基金(70510017)资助
关键词 奇异摄动问题 流线扩散有限元 Bakhvalov—Shishkin网格 singularly perturbed problem Streamline-Diffusion finite element method Bakhvalov-Shishkin mesh
分类号 O241.82 [理学—计算数学]
  • 相关文献

参考文献9

  • 1Johnson C, Saranen J. Streamline Diffusion Methods for the Incompressible Euler and Navier Stocks Equations[J]. Math. Comp., 1986, 47: 118.
  • 2Ling T, Stynes M. The SDFEM on Shishkin meshes for linear convection-diffusion problems[J]. Math. Comp., 2001, 87: 457-484.
  • 3Stynes M, Tobiska L. Analysis of the Streamline-Diffusion Finite Element Method on a shishkin mesh for a Convection-Diffusion Problem with Exponential Layers[J]. J. Mumer. math., 2001, 9: 59-76.
  • 4Stynes M, Tobiskn L. The SDFEM for a convection-diffusion problem with a boundary layer: optimal error analysis and enhancement of accuracy[J]. SIAM. J. Numer. Anal., 2003, 41: 1620- 1642.
  • 5Lint3 T. An upwind difference scheme on a novel Shishkin-type mesh for a linear convection - diffusion problem[J]. J. of comput. Appl. Math., 1999, 110(1): 93-104.
  • 6Roos H G, Stynes M, and Tobisl L. Robust numerical methods for singularly perturbed differ- ential equations: convection-diffusion-reaction and flow problems[M]. Berlin: Spriner 2008.
  • 7Ciarlet P O. The finite element method for elliptic problems[M]. Amsterdam: North-Holland, 2002.
  • 8Zhang Zhimin. Finite element superconvergent approximation for one-dimensional singularly per- turbed problems[J]. Numerical Methods for Partial Differential Equations, 2002, 18: 374-395.
  • 9Zhang Zhimin. Finite element superconvergent on shishkin mesh for 2-D convection-Diffusion problems[J]. Mathematics of computation, 2003, 72: 1147-1177.

同被引文献12

  • 1Hughes T J, Brooks A N. A Multidimensional Upwind Scheme With No Crosswind Diffusion[J]. Finite Element Methods for Convection dominated Flows: ed.By T. J. Hughes, ASME, 1979, 34: 19-35.
  • 2Ling T, Stynes M. The SDFEM on Shishkin meshes for linear convection-diffusion problems[J]. Numer. Math., 2001, 87: 457-484.
  • 3Stynes M, Tobiska L. Analysis of the Streamline-Diffusion Finite Element Method on a shishkin mesh for a Convection-Diffusion Problem with Exponential Layers[J]. J. Numer. Math., 2001, 9: 59-76.
  • 4Stynes M, Tobiska L. The SDFEM for a convection-diffusion problem with a boundary layer: optimal error analysis and enhancement of accuracy[J]. SIAM. J. Numer. Anal., 2003, 41: 1620- 1642.
  • 5DurAn R G, Lombardi A L. Finite element approximation of convection diffusion problems using graded meshes[J]. Appl. Numer. Math., 2006, 56: 1314-1325.
  • 6Lint3 T. The necessity of Shishkin decomposition[J]. Apph Math. Lett., 2001, 14(7): 891-896.
  • 7Ciarlet P G. The finite element method for elliptic problems[M]. Amsterdam: North-Holland, 2002.
  • 8Linfi T. An upwind difference scheme on a novel Shishkin-type mesh for a linear convection - diffusion problem[J]. J. of comput. Appl. Math., 1999, 110(1): 93-104.
  • 9Roos H G, Stynes M and Tobisk L. Robust numerical methods for singularly perturbed differential equations: convection-diffusion-reaction and flow problems[M]. Berlin: Springer, 2008.
  • 10祝鹏,谢资清,周叔子.A COUPLED CONTINUOUS-DISCONTINUOUS FEM APPROACH FOR CONVECTION DIFFUSION EQUATIONS[J].Acta Mathematica Scientia,2011,31(2):601-612. 被引量：6

引证文献2

二级引证文献10

计算数学
2013年 第4期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部