Numerical integration with Taylor truncations for the quadrilateral and hexahedral finite elements
Numerical integration with Taylor truncations for the quadrilateral and hexahedral finite elements
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DOI：
10.1016/j.cam.2006.05.007
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发表时间：
2007-08
影响因子：
2.4
通讯作者：
Shangyou Zhang
中科院分区：
文献类型：
--
作者：
Shangyou Zhang
For general quadrilateral or hexahedral meshes, the finite-element methods require evaluation of integrals of rational functions, instead of traditional polynomials. It remains as a challenge in mathematics to show the traditional Gauss quadratures would ensure the correct order of approximation for the numerical integration in general. However, in the case of nested refinement, the refined quadrilaterals and hexahedra converge to parallelograms and parallelepipeds, respectively. Based on this observation, the rational functions of inverse Jacobians can be approximated by the Taylor expansion with truncation. Then the Gauss quadrature of exact order can be adopted for the resulting integrals of polynomials, retaining the optimal order approximation of the finite-element methods. A theoretic justification and some numerical verification are provided in the paper.
