Negative norm stabilization of convection-diffusion problems

We consider a model convection-diiusion problem in the convection-dominated regine. 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 nite elements or wavelets (while classical SUPG or Galerkin/least-squares methods mimic their eeect through discrete element-by-element weighted L 2-inner products).