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关于Morley元的误差估计

石钟慈   

  1. 中国科学院计算中心
  • 出版日期:1990-02-14 发布日期:1990-02-14

石钟慈. 关于Morley元的误差估计[J]. 计算数学, 1990, 12(2): 113-118.

ON THE ERROR ESTIMATES OF MORLEY ELEMENT

  1. Shi Zhong-ci Computing Center, Academia Sinica
  • Online:1990-02-14 Published:1990-02-14
§1.引言 解薄板弯曲问题的三角形Morley元是六十年代出现的一种非协调元,它的形函数是完整的二次多项式,节点参数是单元顶点上的三个函数值及三边中点上的法向导数值.由于板弯曲问题的常应变是二次多项式,所以这是一个参数最少的非协调板元.由
New error estimates for both moments and rotations are given for the usual Morley plateelement, which are obtained directly using nonconforming finite element techniques that differfrom Arnold-Brezzi approach. The error bound for rotations is better than that of Arnold-Brez-zi, while the bounds for moments in the two different approaches are identical.
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[1] L. S.D. Morley, The triangular equilibrium element in the solution of plate bending problems, Aero.Quart.,19 (1968) , 149-169.
[2] P. Lascaux. P. Lesaint, Some nonconforming finite elements for the plate bending problem, RAIRO Anal.Numer., 9 (1975) , 9-53.
[3] R. Rannacher, On nonconforming and mixed finite elements for plate bending problems. The linear case,RAIRO Anal. Numer, 13(1979) ,369-387.
[4] D. N. Arnold, F. Brezzi, Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates, M~2AN, 19 (1985) , 7-32.
[5] P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.
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