On the nested refinement of quadrilateral and hexahedral finite elements and the affine approximation
On the nested refinement of quadrilateral and hexahedral finite elements and the affine approximation
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DOI：
10.1007/s00211-004-0536-7
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发表时间：
2004-09
影响因子：
2.1
通讯作者：
Shangyou Zhang
中科院分区：
文献类型：
--
作者：
Shangyou Zhang
本文证明了在网格嵌套加密的情况下，用仿射映射代替单元上的Q1映射，可以保持双线性或三线性有限元的最佳逼近性质。新方法截断了参考映射中的二次项和三次项，产生了常数雅可比矩阵和雅可比行列式。这将避免四边形和六面体单元的缺点，其中有理函数的积分必须计算或近似。数值试验验证了分析的正确性。
It is shown in this paper that the optimal approximation property of bilinear or trilinear finite elements would be retained when the affine mapping is used to replace theQ1mapping on each element, if the grids are refined nestedly. The new method truncates the quadratic and cubic terms in reference mappings and produces constant Jacobians and Jacobian matrices. This would avoid a shortcoming of the quadrilateral and hexahedral elements where the integrals of rational functions have to be computed or approximated. Numerical tests verify the analysis.