Explore a 35-minute lecture on error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in 2D. Delve into the formulation of a stabilized quasi-optimal Petrov-Galerkin method based on the variational multiscale approach. Examine the exponential decay of fine-scale correctors and their localization to patch problems dependent on velocity field direction and singular perturbation parameter. Discover how this stabilization ensures stability and quasi-optimal convergence rates for arbitrary mesh Péclet numbers on coarse meshes. Learn about the method's performance, impact of interpolation operators, element patches, and localized multiscale bases through numerical simulations and comprehensive analysis.