Negative norm stabilization of convection-diffusion problems

Abstract We consider a model convection-diffusion problem in the convection-dominated regime. A functional setting is given for stabilized Galerkin approximations, in which the stabilizing terms are based on inner products of the type H − 1 2 . These are explicitly computable via multiscale decompositions such as hierarchical finite elements or wavelets (while classical SUPG or Galerkin/least-squares methods mimic their effect through discrete element-by-element weighted L2-inner products).