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Linear equality constraints in finite element approximation
Author(s) -
Szabo Barna A.,
Kassos Tony
Publication year - 1975
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.1620090306
Subject(s) - mathematics , finite element method , coefficient matrix , simplex algorithm , diagonal , mathematical optimization , system of linear equations , linear programming , basis (linear algebra) , simplex , basis function , diagonally dominant matrix , quadratic equation , block matrix , mathematical analysis , geometry , invertible matrix , pure mathematics , eigenvalues and eigenvectors , physics , quantum mechanics , thermodynamics
The typical numerical problem associated with finite element approximations is a quadratic programming problem with linear equality constraints. When nodal variables are employed, the coefficient matrix of the constraint equations, [ A ], acquires a block‐diagonal structure. The transformation from polynomial coefficients to nodal variables involves finding a basis for [ A ] and computing its inverse. Simultaneous satisfaction of completeness and C 1 (or higher) continuity requirements establishes linear relationships among the nodal variables and precludes inversion of the basis by exclusively element‐level operations. Linear dependencies among the constraint equations and among the nodal variables can be evaluated by the simplex method. The computational procedure is outlined.