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ADAPTIVE FINITE ELEMENT METHOD AND LOCAL MULTIGRID METHOD FOR ELASTICITY PROBLEMS

LIU Chun-mei1, XIAO Ying-xiong2, SHU Shi1, ZHONG Liu-qiang3   

  1. 1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, China;
    2. Civil Engineering and Mechanics College, Xiangtan University, Xiangtan, Hunan 411105, China;
    3. School of Mathematical Sciences, South China Normal University, Guangzhou, Guangdong 510631, China
  • Received:2010-12-17 Revised:2011-07-21 Online:2012-09-25 Published:2012-09-25
  • Contact: xiao ying-xiong E-mail:xyx610xyx@yahoo.com.cn

Abstract:

In this paper, an adaptive finite element (AFEM) method is designed by using the newest vertex bisection for linear elasticity problems in two dimensions. This method marks exclusively according to the error estimator without special treatment of oscillation and performs a minimal element refinement without the interior node property. Furthermore, a type of multigrid method based on the local relaxation is applied to the AFEM discrete systems by using the special properties during refinement. The results of various numerical experiments are shown that the proposed AFEM method is uniformly convergent and has quasi-optimal numerical complexity. The resulting multigrid method is much more robust and efficient in CPU times than the usual multigrid methods.

Key words: elasticity problems, adaptive finite element method, quasi-optimal complexity, local relaxation, multigrid method

CLC Number: 

  • O343.3
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