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用有限元解奇异摄动边值问题的移动网格算法

A Moving Mesh Algorithm Based on FEM for Singularly Perturbed Boundary Value Problems
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摘要 考虑一类奇异摄动边值问题.为了对其数值求解,与文[1,2]不同的是,采用基于有限元方法的移动网格算法.采用的网格有(N+1)个节点并初始化为均匀网格,其节点采用一种迭代算法来自适应移动,该算法等分布分片线性数值解函数弧长.用数值试验证实了该方法产生的数值解是关于摄动参数ε一致收敛的. Akind of singularly perturbed boundary value problem is investigated. A moving mesh algorithm based on finite element method is applied. The mesh has a fixed number（N＋1） of nodes and is initially uniform, but its nodes are moved adaptively by using an iterative algorithm based on equidistribution of the arc-length of the current computed piecewise linear solution. Numerical experiments are carried out, which testifies that the approximations are uniformly convergent with the perturbation parameter.
作者 杨继明
机构地区 湖南工程学院理学院
出处 《湖南工程学院学报（自然科学版）》 2008年第3期46-48,共3页 Journal of Hunan Institute of Engineering(Natural Science Edition)
基金 湖南省教育厅科研资助项目(07C219)
关键词 奇异摄动 有限元 移动网格 等分布 singularly perturbed finite element moving mesh equidistribution
分类号 O151.21 [理学—基础数学]
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参考文献6

  • 1杨继明.用等分布原理求解一类奇异摄动两点边值问题的数值算法[J].湖南工程学院学报（自然科学版）,2004,14(2):84-87. 被引量：4
  • 2杨继明,陈艳萍.一类奇异摄动对流扩散边值问题的移动网格方法[J].湘潭大学自然科学学报,2004,26(3):24-29. 被引量：12
  • 3G. Beckett and J. A. Mackenzie,On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution[J]. J. Comput. Appl. Math. , 2001,131 : 381 -- 405.
  • 4Yanping Chen, Uniform convergence analysis of finite difference approximations for singular perturbation problems on an adapted grid[J]. Advances in Computational Mathematics, 2006,24 (1-- 14) :197--212.
  • 5NATALIA KOPTEVA and MARTIN STYNES, A robust adaptive method for a quasi-linear one dimensional convection--diffusion problem[J]. SIAM J. Numer. Anal. , 2001,39 (4) : 1446-- 1467.
  • 6T. Linss, Uniforming pointwise convergence of finite difference schemes using grid equidistrihution [J]. Computing, 2001,66 : 27--39.

二级参考文献17

  • 1[6]J.J.H. Miller, E. O' Riordan, G. I. Shishkin. Solution of singularly perturbed problems with ε- uniform numerical methods-Introduction to the theory of linear problems in one and two dimensions[ M]. World Scientific, Singapore,1996.
  • 2[7]Y. Qiu,D. M. Sloan, T. tang. Numerical solution of a singularly perturbed two-point boundary value problem using equidistribution: analysis of convergence [J ]. J. Comput.Appl. Math. ,2000,116:121 - 143.
  • 3[8]White, A. B. On selection of equidistributing meshes for two-point boundary problems[ J ]. SIAM J. Numer. Anal.1979,16:472 - 502.
  • 4[1]G. Beckett. The robust and efficient numerical solution of singularly perturbed boundary value problems using gird adaptivity [ J ]. Ph. D. thesis, University of Strathclyed,1999.
  • 5[2]Yanping Chen. Uniform convergence analysis of finite difference approximations of a singularly perturbed boundary value problem on an adapted grid, (in press).
  • 6[3]N. KOPTEVA. Maximum norm a posteriori error estimates for a one-dimensional convection diffusion problem[J]. SIAM J. Numer. Anal. ,2001,39:423 - 441.
  • 7[4]NATALLA KOPTEVA, MARTIN STYNES. A robust adaptive method for a quasi-linear one dimensional convection- diffusion problem [ J ]. SIAM J. Numer. Anal,2001,39(4) :1446 - 1467.
  • 8[5]Torsten Linβ. Uniform pointwise convergence of finite difference schemes using grid equidistribution [ J ]. Computing, 2001,66 ( 1 ): 27 - 39.
  • 9Beckett G,Mackenzie J A.Convergence analysis of finite difference approximations on equidistributed grids to a singularly perturbed boundary value problem[J].Appl Numer Math,2000,35:87-109.
  • 10Yanping Chen.Uniform convergence analysis of finite difference approximations for singularly perturbed problems on an adapted grid[J]. Submitted to Advances in Computational Mathematics.

共引文献11

湖南工程学院学报（自然科学版）
2008年 第3期

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