Negative norm stabilization of convection-diffusion problems

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 hierarchic al finite elements or wavelets (while classical SUPG or Galerkin/least-squares methods mimic their effect through discrete element-by-element weighted L-2-inner products). (C) 2000 Elsevier Science Ltd. Ail rights reserved.