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Analytical integration formulae for linear isoparametric finite elements
Author(s) -
Babu D. K.,
Pinder G. F.
Publication year - 1984
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620200613
Subject(s) - quadrilateral , gaussian quadrature , finite element method , bilinear interpolation , mathematics , numerical integration , quadrature (astronomy) , gauss–kronrod quadrature formula , gaussian , basis (linear algebra) , basis function , mathematical analysis , geometry , nyström method , integral equation , structural engineering , engineering , statistics , physics , electrical engineering , quantum mechanics
Exact and approximate analytical expressions can be derived for integrals arising in finite element methods, employing isoparametric linear quadrilaterals in two space dimensions with bilinear basis functions. The formulae associated with rectangular elements, arbitrarily oriented in space, can be shown to be a special case. The proposed method provides considerable savings in computational effort, in comparison with a numerical method that employs Gaussian quadrature procedures. In addition, the method, when applied to a quadrilateral inscribable in a circle, can be shown to produce better accuracy than the associated (2 × 2) Gaussian quadrature formulae.