کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4642870 1341359 2007 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Numerical integration with Taylor truncations for the quadrilateral and hexahedral finite elements
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Numerical integration with Taylor truncations for the quadrilateral and hexahedral finite elements
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 205, Issue 1, 1 August 2007, Pages 325–342
نویسندگان
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