Application of the variational Germano identity to the variational multiscale formulation

Abstract

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.