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

作　　者：Xuying Zhao Zhong-Ci Shi 

机构地区：[1]LSEC,Institute of Computational Mathematics and Scientific/Engineering Computing,NCMIS,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [2]School of Mathematical Sciences,Capital Normal University,Beijing 100048,China

出　　处：《Science China Mathematics》2019年第12期2591-2616,共26页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11671390);supported by National Natural Science Foundation of China(Grant No.11371359)

摘　　要：Nonconforming grids with hanging nodes are frequently used in adaptive finite element comput at ions.In all earlier works on such methods,proper cons train ts 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.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.

关 键 词：adaptive finite ELEMENT a POSTERIORI error estimate hexahedral NONCONFORMING ELEMENT hangingnode 

分 类 号：O15[理学—数学]