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四边形单元h-收敛误差估计的探讨*

段梅 宫本裕 周本宽 陈大鹏

段梅, 宫本裕, 周本宽, 陈大鹏. 四边形单元h-收敛误差估计的探讨*[J]. 应用数学和力学, 1995, 16(12): 1043-1050.
引用本文: 段梅, 宫本裕, 周本宽, 陈大鹏. 四边形单元h-收敛误差估计的探讨*[J]. 应用数学和力学, 1995, 16(12): 1043-1050.
Duan Mei, Miyamoto Yutaka, Zhou Benkuan, Chen Dapeng. On the Error Estimate of h-Convergence in Quadrilateral Elements[J]. Applied Mathematics and Mechanics, 1995, 16(12): 1043-1050.
Citation: Duan Mei, Miyamoto Yutaka, Zhou Benkuan, Chen Dapeng. On the Error Estimate of h-Convergence in Quadrilateral Elements[J]. Applied Mathematics and Mechanics, 1995, 16(12): 1043-1050.

四边形单元h-收敛误差估计的探讨*

基金项目: * 国家自然科学基金和博士点基金

On the Error Estimate of h-Convergence in Quadrilateral Elements

  • 摘要: 本文证明了四边形单元的h-收敛性,给出了相应的引理和定理,讨论了误差估计问题,为四边形单元h-收敛自适应有限元分析准备了基础。
  • [1] P.G.Cialet.The Finite Element method for Elliptic Problems.NorthHolland.Amsterdam(1978).
    [2] G.Strang and G.F.Fix,An Analysis of the Finite Element Method.Prentice-Hall.Englewood Cliffs.N.J.(1973).
    [3] I.Babuska and A.K.Aziz,Survey lecture on the mathematical foundation of the finite element method.in The Mathematical Foundations of the FEM with Applications to Partial Differential Equations.Ed.A.K.Aziz Academic Press.N.Y.(1972),3-382.
    [4] M.K.Georges and M.S.Shephard,Automated adaptive two-dimensional system for the hp-version of the finite element method,Int.J.Num.Mettt.Eng.,32.4(1991).
    [5] I.Babuska,R.B.Kellogy and J.Pitkaranta.Direct and inverse error estimates for finite element with mesh refinements.Numer.Math.,33(1979).447-471.
    [6] W.Gui and I.Babuska,The h.p and h-P version of the finite element method in one dimension,Part III-the adaptive h-p version.Numer.Math.,49(1988),659-684.
    [7] I.Babuska and M.Vogelius,Feedback and adaptive finite element solution of one dimensional boundary value problems,Numer.Math.,44(1984).75-102.
    [8] D.W.Wang,I.N.Katz and B.A.Szabo h-and p-version finite element analysis of a rhombic plate.Int.J.Num.Eng.,20(1984),1399-1405.
    [9] J.Z.Zhu and O.C.Zienkiewicz,Adaptive techniques in the finite element method.Commun.Appl.Numer.Meth.,4(1988),197204.
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出版历程
  • 收稿日期:  1995-03-02
  • 刊出日期:  1995-12-15

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