Negative norm stabilization of convection-diffusion problems

We consider a model convection-diffusion problem in the convection-dominate d regime. A functional setting is given for stabilized Galerkin approximati ons, 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 hierarchic al finite elements or wavelets (while classical SUPG or Galer kin/least-squares methods mimic their effect through discrete element-by-el ement weighted L-2-inner products). (C) 2000 Elsevier Science Ltd. Ail righ ts reserved.