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Accuracy of least-squares methods for the Navier-Stokes equationsRecently there has been substantial interest in least-squares finite element methods for velocity-vorticity-pressure formulations of the incompressible Navier-Stokes equations. The main cause for this interest is the fact that algorithms for the resulting discrete equations can be devised which require the solution of only symmetric, positive definite systems of algebraic equations. On the other hand, it is well-documented that methods using the vorticity as a primary variable often yield very poor approximations. Thus, here we study the accuracy of these methods through a series of computational experiments, and also comment on theoretical error estimates. It is found, despite the failure of standard methods for deriving error estimates, that computational evidence suggests that these methods are, at the least, nearly optimally accurate. Thus, in addition to the desirable matrix properties yielded by least-squares methods, one also obtains accurate approximations.
Document ID
19930020019
Acquisition Source
Legacy CDMS
Document Type
Technical Memorandum (TM)
Authors
Bochev, Pavel B. (Virginia Polytechnic Inst. and State Univ. Blacksburg., United States)
Gunzburger, Max D. (NASA Lewis Research Center Cleveland, OH, United States)
Date Acquired
September 6, 2013
Publication Date
June 1, 1993
Subject Category
Fluid Mechanics And Heat Transfer
Report/Patent Number
NASA-TM-106209
NAS 1.15:106209
ICOMP-93-19
E-7919
Accession Number
93N29208
Funding Number(s)
CONTRACT_GRANT: NCC3-233
PROJECT: RTOP 505-90-5K
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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