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Error Analysis of a Variational Multiscale Stabilization for Convection-Dominated Diffusion Equations in 2D
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- 1 Overview
- 2 Background
- 3 Motivation
- 4 Brief literature on multiscale methods
- 5 Upper bounds in V and Vb
- 6 Spectral gap under certain assumption
- 7 Conformal Galerkin approximation
- 8 Performance of the Galerkin approximation
- 9 State of art methods
- 10 Nodal interpolation based VMS
- 11 An illustration of multiscale test bases
- 12 Impact of the choice of interpolation operators
- 13 Element patches
- 14 Element correctors and localized multiscale bases
- 15 An illustration of the localized multiscale test bases
- 16 Localized VMS for the model problem
- 17 Numerical simulation
- 18 Conclusion 2
