]*>","")" /> 非嵌套网格上的Morley元两水平加性Schwarz方法

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非嵌套网格上的Morley元两水平加性Schwarz方法

石钟慈,谢正辉   

  1. 中国科学院计算数学与科学工程计算研究所,科学与工程计算国家重点实验室,中国科学院大气物理研究所
  • 出版日期:1997-03-14 发布日期:1997-03-14

石钟慈,谢正辉. 非嵌套网格上的Morley元两水平加性Schwarz方法[J]. 计算数学, 1997, 19(3): 313-328.

A TWO-LEVEL ADDITIVE SCHWIRZ METHOD FOR MORLEY ELEMENT ON NONESTED MESHES

  1. Shi Zhong-ci(State Key Laboratory Of Scientific/Engineering Computing,Institute of Computational Mathematics and Scientific/Engineering Computing,Chinese Academy of Sciences, Beijing)Xie Zheng-hui(LASG, Institute of Atmospheric Physics, Chinese Academy of
  • Online:1997-03-14 Published:1997-03-14
In this paper, we develop a two-level additive Schwarz preconditioner for Morley element using nonnested meshes. We define an intergrid transfer operator that satisfies certain stable approximation properties by using a conforming interpolation operator and construct a uniformly bounded decomposition for the finite element space. Both coarse and fine grid spaces are nonconforming. We get optimal convergence properties of the additive Schwarz algorithm that is constructed on nonnested meshes and with a not necessarily shape regular subdomain partitioning. Our analysis is based on the theory of Dryja and Widlund.It is interesting to mention that when coarse and fine spaces are all nonconforming, a natural intergrid operator seems to be one defined by taking averages of the nodal parameters. In this way, we obtain the stable factor (H/h)3/2, and show that this factor can not be improved. However, to get an optimal preconditioner,we need in general the stability with a factor C independent of mesh parameters.Therefore. the latter can not be used in this case.
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