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On penalty function methods in the finite‐element analysis of flow problems
Author(s) -
Reddy J. N.
Publication year - 1982
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.1650020204
Subject(s) - penalty method , finite element method , mathematics , equivalence (formal languages) , mathematical optimization , stokes flow , convergence (economics) , context (archaeology) , navier–stokes equations , flow (mathematics) , compressibility , geometry , physics , mechanics , paleontology , discrete mathematics , economics , thermodynamics , economic growth , biology
In this paper the penalty function method is reviewed in the general context of solving constrained minimization problems. Mathematical properties, such as the existence of a solution to the penalty problem and convergence of the solution of a penalty problem to the solution of the original problem, are studied for the general case. Then the results are extended to a penalty function formulation of the Stokes and Navier‐Stokes equations. Conditions for the equivalence of two penalty‐finite element models of fluid flow are established, and the theoretical error estimates are verified in the case of Stokes's problem.