Hexahedral constraint-free finite element method on meshes with hanging nodes

  • Xuying ZhaoEmail author
  • Zhong-Ci Shi


Nonconforming grids with hanging nodes are frequently used in adaptive finite element computations. In all earlier works on such methods, proper constraints should be enforced on degrees of freedom on edges/faces with hanging nodes to keep continuity, which yield numerical computations much complicated. In 2014, Zhao et al. (2014) presented quadrilateral constraint-free finite element methods on quadrilateral grids with hanging nodes. This paper further develops a hexahedral constraint-free finite element method on hexahedral grids with hanging nodes, which is of greater challenge than the two-dimensional case. Residual-based a posteriori error reliability and efficiency are also established in this paper.


adaptive finite element a posteriori error estimate hexahedral nonconforming element hanging node 


65N30 65N15 35J25 


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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, NCMIS, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina

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