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The condition of the least‐squares finite element matrices
Author(s) -
Fried Isaac
Publication year - 2015
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.5146
Subject(s) - finite element method , a priori and a posteriori , mathematics , stiffness matrix , least squares function approximation , stiffness , matrix (chemical analysis) , element (criminal law) , direct stiffness method , mathematical analysis , mathematical optimization , structural engineering , engineering , statistics , materials science , philosophy , epistemology , estimator , political science , law , composite material
Summary A universal, practical, a priori, numerical procedure is presented by which to realistically bind the spectral condition number of the global stiffness matrix generated by the finite element least‐squares method. The procedure is then applied to second and fourth‐order problems in one and two dimensions to show that the condition of the global stiffness matrix thus generated is, in all instances, proportional to but the diameter of the element squared. Copyright © 2015 John Wiley & Sons, Ltd.