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Variable penalty method for finite element analysis of incompressible flow
Author(s) -
Kheshgi Haroon S.,
Scriven L. E.
Publication year - 1985
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650050903
Subject(s) - penalty method , finite element method , discretization , mathematics , truncation error , constant (computer programming) , flow (mathematics) , mixed finite element method , mathematical analysis , incompressible flow , compressibility , boundary (topology) , truncation (statistics) , mathematical optimization , geometry , computer science , mechanics , physics , statistics , thermodynamics , programming language
A new scheme is applied for increasing the accuracy of the penalty finite element method for incompressible flow by systematically varying from element to element the sign and magnitude of the penalty parameter λ, which enters through ∇.v + p /λ = 0, an approximation to the incompressibility constraint. Not only is the error in this approximation reduced beyond that achievable with a constant λ, but also digital truncation error is lowered when it is aggravated by large variations in element size, a critical problem when the discretization must resolve thin boundary layers. The magnitude of the penalty parameter can be chosen smaller than when λ is constant, which also reduces digital truncation error; hence a shorter word‐length computer is more likely to succeed. Error estimates of the method are reviewed. Boundary conditions which circumvent the hazards of aphysical pressure modes are catalogued for the finite element basis set chosen here. In order to compare performance, the variable penalty method is pitted against the conventional penalty method with constant λ in several Stokes flow case studies.