Advances in Computational Mathematics

, Volume 25, Issue 1, pp 287-304

First online:

An algebraic multigrid method for finite element systems on criss-cross grids

  • Shi ShuAffiliated withInstitute for Computational and Applied Mathematics of Xiangtan University
  • , Jinchao XuAffiliated withDepartment of Mathematics and Center for Computational Mathematics and Application of Pennsylvania State University
  • , Ying YangAffiliated withInstitute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences
  • , Haiyuan YuAffiliated withInstitute for Computational and Applied Mathematics of Xiangtan University

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In this paper, we design and analyze an algebraic multigrid method for a condensed finite element system on criss-cross grids and then provide a convergence analysis. Criss-cross grid finite element systems represent a large class of finite element systems that can be reduced to a smaller system by first eliminating certain degrees of freedoms. The algebraic multigrid method that we construct is analogous to many other algebraic multigrid methods for more complicated problems such as unstructured grids, but, because of the specialty of our problem, we are able to provide a rigorous convergence analysis to our algebraic multigrid method.


algebraic multigrid method finite element criss-cross grids convergence analysis