JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (08): 34-39.doi: 10.6040/j.issn.1671-9352.0.2015.055

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Local multigrid method for higher-order finite element discretizations of elasticity problems in two dimensions

LIU Chun-mei1, ZHONG Liu-qiang2, SHU Shi3, XIAO Ying-xiong4   

  1. 1. Institute of Computational Mathematics, College of Science, Hunan University of Science and Engineering, Yongzhou 425199, Hunan, China;
    2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, Guangdong, China;
    3. School of Mathematical and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, China;
    4. College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan 411105, Hunan, China
  • Received:2015-02-02 Online:2015-08-20 Published:2015-07-31

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Abstract: Due to few limited vertexes increase during every refinement of adaptive finite element method (AFEM), only some limited basis functions change between two finite element spaces based on two adjacent refinement meshes. By use of this special property, a type of multigrid method based on the local relaxation is applied to the high-order AFEM discrete systems of elasticity problems in two dimensions, that is, during each iteration, the part of the homogeneous high-order systems based on hierarchical basis functions is solved by a symmetric Gauss-Seidal method once, and then these residual systems are projected onto linear finite element space, and discrete systems based on linear finite element spaces are generated. Finally, these linear finite element discretizations are solved by a symmetric local Gauss-Seidal method once. The numerical experiments show that the local multigrid method is robust.

Key words: elasticity problems, higher-order finite element discretizations, local relaxation, multigrid method

CLC Number: 

  • O241.8
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