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Singular capacity matrices produced by low‐order Gaussian integration in the finite element method
Author(s) -
Jackson C. P.
Publication year - 1981
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.1620170605
Subject(s) - gaussian quadrature , finite element method , gauss , mathematics , gaussian , gaussian integral , mixed finite element method , extended finite element method , basis (linear algebra) , mathematical analysis , element (criminal law) , matrix (chemical analysis) , gaussian elimination , basis function , order (exchange) , quadrature (astronomy) , finite element limit analysis , geometry , integral equation , physics , structural engineering , engineering , nyström method , materials science , law , quantum mechanics , political science , optics , composite material , finance , economics
This paper considers some consequences of the common implementation of the finite element method in which element integrals are evaluated numerically by Gaussian quadrature. It shows that if the order of the Gauss scheme is less than the number of basis functions on an element, then the numerically evaluated capacity matrix for that element is singular. The capacity matrix of an assembly of such elements is also considered and is shown to be singular under certain conditions.