Variational Multiscale Analysis: the Fine-scale Green's Function, Projection, Optimization, Localization, and Stabilized Methods

By Thomas J. R. Hughes, Giancarlo Sangalli. SIAM Journal on Numerical Analysis, 2007

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A UNIFIED CONVERGENCE ANALYSIS FOR LOCAL PROJECTION STABILISATIONS APPLIED TO THE OSEEN PROBLEM (2007, background): “It is well known that stabilised methods can also be derived from a variational multiscale formulation [24–26 , 40].”
A robust SUPG norm a posteriori error estimator for stationary convection-diffusion equations (2013, background): “It can be applied to stabilized discretizations since their error distribution is practically local [13].”
Improving stability of stabilized and multiscale formulations in flow simulations at small time steps (2010, unknown): “Recently τ’s were identified with low-order moments of the fine-scale Green’s function, a fundamental object in the design and analysis of variational multiscale methods (see [13]).”
Adaptivity and variational stabilization for convection-diffusion equations∗ (2012, background): “Examples are low parameter models, Large Eddy Simulation or modern variants such as Variational Multiscale Method and Subgrid Modeling.”
Stabilized space–time computation of wind-turbine rotor aerodynamics (2011, methodology): “Mathematical analysis of the method was performed in [96].”