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Some criteria for numerically integrated matrices and quadrature formulas for triangles
Author(s) -
Laursen M. E.,
Gellert M.
Publication year - 1978
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.1620120107
Subject(s) - quadrature (astronomy) , mathematics , finite element method , gauss–kronrod quadrature formula , numerical integration , tanh sinh quadrature , clenshaw–curtis quadrature , limiting , gaussian quadrature , gauss–jacobi quadrature , sampling (signal processing) , mathematical analysis , nyström method , computer science , integral equation , structural engineering , engineering , mechanical engineering , electrical engineering , filter (signal processing) , computer vision
For a wide calss of finite element matrices integrated numerically rather than exactly, a definable number of sampling points is found to be sufficient for keeping their theoretical properties unchanged. A systematic criterion limiting the number of possible point configurations for numerical quadrature formulas on triangles is established. Some new high order formulas are presented. Tables containing optional formulas with respect to minimum number of sampling points and required degrees of accuracy are given. They are arranged so as to assist with selection of suitable quadrature formulas for finite element computer programming.