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Application of the variational Germano identity to the variational multiscale formulation
Author(s) -
Oberai A. A.,
Sondak D.
Publication year - 2011
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1379
Subject(s) - connection (principal bundle) , space (punctuation) , computer science , identity (music) , construct (python library) , mathematics , scale (ratio) , mathematical optimization , geometry , physics , quantum mechanics , acoustics , programming language , operating system
We examine the connection between the variational multiscale (VMS) formulation and the variational counterpart of the Germano identity (VGI). We note that they are both based on the same multiscale construct of a given coarse scale space and a user‐defined projector into this space, which defines the desired numerical solution. By utilizing this connection we demonstrate how the VGI may be used to determine parameters for the models derived using the VMS formulation. Copyright © 2010 John Wiley & Sons, Ltd.