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

奇异摄动罗宾问题在Bakhvalov-Shishkin网格上的一致收敛有限差分法 被引量：5

Uniform convergence analysis of a singularly perturbed Robin problem on a Bakhvalov-Shishkin mesh.
下载PDF
导出
摘要 考虑一个奇异摄动罗宾问题在Bakhvalov-Shishkin网格上的迎风差分策略,得到在改进的Shishkin网格上迎风策略是关于ε一致的一阶L∞模收敛的.数值实验证实了此理论结果,显示估计是稳健的. An upwind finite difference scheme is considered on a Bakhvalov-Shishkin mesh for a singularly perturbed Robin problem. It is proved that the upwind scheme on the modified Shishkin mesh is first-order convergent in the discrete L~∞ norm, independently of the diffusion parameter ε. Numerical experiments support these theoretical results and indicate that the estimates are sharp.
作者 岑仲迪 高怀毅
机构地区 浙江大学数学系 宁夏大学数学系
出处 《浙江大学学报（理学版）》 CAS CSCD 2004年第4期373-375,386,共4页 Journal of Zhejiang University（Science Edition）
关键词 罗宾问题 奇异摄动 迎风策略 Bakhvalov-Shishkin网格 Robin problem singular perturbation upwind scheme Bakhvalov-Shishkin mesh
分类号 O175.1 [理学—基础数学] O241.81 [理学—计算数学]
  • 相关文献

参考文献9

  • 1CHANG K W, HOWES F A. Nonlinear Singular Perturbation Phenomena: Theory and Applications[M]. New York: Springer-Verlag,1984.
  • 2DOOLAN E P, MILLER J J H, SCHILDERS W H A. Uniform Numerical Methods for Problems with Initial and Boundary Layer [M]. Dublin: Boole Press,1980.
  • 3MORTON K W. Numerical Solution of ConvectionDiffusion Problems[M]. Londan: Chapman & Hall,1996.
  • 4ROOS H G, STYNES M, TOBISKA L. Numerical Methods for Singularly Perturbed Differential Equation[M]. Berlin: Springer-Verlag,1996.
  • 5NATESAN S, RAMANUJAM N. An asymptotic-numerical method for singularly perturbed Robin problems-I[J]. Appl Math Comp, 2002, 126 (1):97-107.
  • 6KELLOGG R B, TSAN A. Analysis of some difference approximations for a singular perturbation problem without turning points [J ]. Math Comp, 1978,32(144): 1025-1039.
  • 7ROOS H G, LINβ T. Sufficient conditions for uniform convergence on layer-adapted grids [J]. Computing, 1999,63(1):27-45.
  • 8梁克维,李大明,江金生.中点迎风差分格式在Bakhvalov-Shishkin网格上的注记[J].浙江大学学报（理学版）,2002,29(1):20-24. 被引量：8
  • 9金中秋,梁克维,江金生.修正的Bakhvalov-Shishkin网格上奇异摄动问题的一致收敛性[J].浙江大学学报（理学版）,2003,30(3):263-267. 被引量：2

二级参考文献11

  • 1SHISHKIN G I. Difference scheme for a singularly perturbed parabolic equation with discontinuous boundary condition(in Russian)[J]. J Comput Math Phys, 1988,28(11): 1649--1662.
  • 2SHISHKIN G I. Grid approximation of singularly perturbed elliptic and parabolic equations . Moseow:Keldysh Institute, 1990.
  • 3MILLER J J H, O'RIORDAN E, SHISHKIN G I.Solution of Singularly Perturbed Problems with ε-uni-formed Numerical Methods-introduction to the Theory of Linear Problems in One and Two Dimensions[M].Singapore : World Scientific, 1996.
  • 4DONALD, SMITH R. Singularly Perturbed Theory [M]. Cambridge : Cambridge University Press, 1985.
  • 5HIRT C W, RAMSHAW J D. Prospects for numerial simulation of bluff-body aerodynamics . Aerodynamic Drag Mechanisms of Bluff Bodies and Road Vehicles . New York: PLENUM, 1978. 313--355.
  • 6ROACHE P J. Computational Fluid Dynamics [M].Albuquerque: Hermosa, 1972. 295.
  • 7HOFFMAN Joe D. Relationship between the truncation errors of centered finite difference approximations on uniform and nonuniform meshes[J]. J of Computational Physics, 1982,46(3): 469--474.
  • 8LINB T. An upwind difference scheme on a novel shishkin-type mesh for a linear convection-diffusion problem[J]. J Comput Appl Math, 1999,110(1) :93--104.
  • 9LINB T. Analysis of a galerkin finite element method on a bakhvalov-shishkin mesh for a linear convection-diffusion problem [J]. IMA J NumerAnal, 2000,20(4) : 621 -- 632.
  • 10梁克维,金中秋,李大明.关于ε一致的奇异摄动问题的差分格式及其收敛速度[J].浙江大学学报（理学版）,2000,27(5):473-476. 被引量：6

共引文献7

同被引文献30

  • 1ISRAELI M, UNGARISH M. Improvement of numerical solution of boundary layer problems by incorporation of asymptotic approximations [J]. Numer Math, 1982,39(3) :309-324.
  • 2NATESAN S, RAMANUJAM N. A "Booster method" for singular perturbation problems arising in chemical reactor theory[J]. Applied Mathematics and Computation, 1999,100 (1) 27- 48.
  • 3UNGARISH M. Combination of Asymptotic and Numerical Methods for the Investigation of Rotating Compressible Flows in a Cylinder for Small Rossby and Ekman Numbers[D]. Haifa: Technion, Israel Institute of Technology, 1980.
  • 4ISRAELI M, UNGARISH M. Improvement of numerical schemes by incorporation of approximate solutions applied to rotating compressible flows [A].Proceedings of the Seventh International Conference on Numerical Methods in Fluid Dynamics[C]. Stanford: Stanford University, 1980.
  • 5KELLOGG R B, TSAN A. Analysis of some difference approximations for a singular perturbation problem without turning points[J]. Math of Comp, 1978,144(32): 1025- 1039.
  • 6PROTTER M H, WEINBERGER H F. Maximum Primciples in Differential Equations[M]. N J :Prentice-Hall, Englewood Cliffs, 1967.
  • 7CHANG K W, HOWES F A. Nonlinear Singular Perturbation Phenomena: Theory and Applications [M].New York: Springer-Verage,1984.
  • 8DOOLAN E P, MILI.ER J J H, SCHILDERS W H A.Uniform Numerical Methods for Problems with Initial and Boundary Layer [M]. Dublin: Boole Press, 1980.
  • 9MORTON K W. Numerical Solution of Convection-diffusion Problems[M]. Londan: Chapman & Hall,1996.
  • 10ROOS H G, STYNES M, TOBISKA L. Numericalmethods for singularly perturbed differential equation[C]//Springer Series in Computational Mathematics.Berlin: Springer-Verage, 1996.

引证文献5

二级引证文献7

浙江大学学报（理学版）
2004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