Multiscale stabilization

In this chapter, we discuss multiscale stabilizationMultiscale stabilization following [69] on the example of multiscale convection-dominated diffusionConvection-dominated diffusion with a high Peclet numberPeclet number. In these systems, besides finding a reduced order model, one needs to stabilize the system to avoid large errors [355]. Stabilization of multiscale methods for convection-diffusion cannot simply use a modified diffusion and requires more sophisticated techniques. In this chapter, we discuss an application of the GMsFEM in developing a Petrov-Galerkin method (e.g., [147, 337, 338]).