Negative Norm Stabilization of Convection-Diffusion Problems

S. Bertoluzza, C. Canuto and A. Tabacco

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 a Sobolev space of order -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).

Appl. Math. Lett. 13, (2000), 121--127.

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