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Penalty‐function iterative procedures for mixed finite element formulations
Author(s) -
Felippa C. A.
Publication year - 1986
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.1620220120
Subject(s) - penalty method , finite element method , displacement (psychology) , mathematics , iterative method , convergence (economics) , lagrange multiplier , function (biology) , mixed finite element method , mathematical optimization , stiffness , mathematical analysis , structural engineering , engineering , psychology , evolutionary biology , economics , psychotherapist , biology , economic growth
Iterative methods for solving mixed finite element equations that correct displacement and stress unknowns in ‘staggered’ fashion are attracting increased attention. This paper looks at the problem from the standpoint of allowing fairly arbitrary approximations to be made on both the stiffness and compliance matrices used in solving for the corrections. The resulting iterative processes usually diverge unless stabilized with Courant penalty terms. An iterative procedure previously constructed for equality‐constrained displacement models is recast to fit the mixed finite element formulation in which displacements play the role of Lagrange multipliers. The penalty function iteration is shown to reduce to an ordinary staggered stress‐displacement iteration if the weight is set to zero. Convergence conditions for these procedures are stated and the potentially troublesome effect of prestress modes noted.