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二阶奇异摄动问题的高阶有限体积法 被引量:1

High Order Finite Volume Methods for the Second Order Singular Perturbation Problems
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摘要 建立一种奇异摄动两点边值问题数值求解的高阶Hermite型有限体积法,给出该体积法的1个简单的计算格式,在较弱的条件下得到最佳阶的一致收敛性估计,并用数值实验验证该有限体积法的合理性和方法的有效性.结果表明,有限体积法和Galerkin方法几乎具有相同精度,最优收敛阶的实际值与理论值很接近. A high order finite volume method of the Hermite type is established for solving the second order singular perturbation problems. A simple computing scheme of finite volume method is presented. The optimal order of uniform convergence is obtained under a much weaker condition than coercivity assumption. Numerical experiments are presented to verify our theoretical estimates. It shows that finite volume method and Galerkin method have nearly the same accuracy and the optimal order of uniform convergence ealeulated from the numerical errors is very closed to theoretical value.
作者 何崇南
出处 《广西科学》 CAS 2009年第4期392-396,399,共6页 Guangxi Sciences
基金 国家自然科学基金项目(10962001) 广西自然科学基金资助项目(0575029)资助
关键词 奇异摄动问题 有限体积法 最优网格 singular perturbation problems, finite volume method,optimal meshes
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  • 1Stynes M, E O'Riordan. A finite element method for a singularly perturbed boundary value problem[J].Numer Math,1986,50: 1-15. 被引量:1
  • 2Stynes M ,E O'Riordan. An analysis of a singularly perturbed two-point boundary value problem using only finite element techniques[J]. Math Comp, 1991,56 : 663- 675. 被引量:1
  • 3Sun G,Stynes M. Finite element methods for singularly perturbed high order elliptic two point boundary problems, I:Reaction-diffusion type problems [J].IMA J Numer Anal,1995,15:117-139. 被引量:1
  • 4Sun G,Stynes M. Finite element methods for singularly perturbed high order elliptic two point boundary problems, Ⅱ : Convection diffusion-type problems [J]. IMA J Numer Anal,1995,15:197- 219. 被引量:1
  • 5Liu W,Tang T. Error analysis for a Galerkinspectral method with coordinate transformation for solving singularly perturbed problems [J].Appl Numer Math, 2001,38 : 315-345. 被引量:1
  • 6H J J Miller,E O'Riordan ,G I Shishkin. Fitted numerical methods for singularly perturbation problems [M]. Singapore:World Scientific, 1996. 被引量:1
  • 7Tang T,Trummer M R. Boundary layer resolving pseudospectral methods for singular perturbation problems[J]. SIAM J Sci Comput, 1996,17 : 430-438. 被引量:1
  • 8Qiu Y,Sloan D M. Analysis of difference approximations to a singular perturbed two point boundary value problem on an adaptively generated grid[J]. J Comput Appl Math, 1999,101 : 1-25. 被引量:1
  • 9Roos H G,Stynes M,Tobiska L. Numerical methods for singularly perturbed differential equations [M]. Berlin Springer-Verlag, 1996. 被引量:1
  • 10Shishkin G I. Grid approximation of singularly perturbed parabolic equations with internal layers[J]. Soy J Numer Anal Math Model, 1988,3:393-407. 被引量:1

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