PUMA
Istituto di Matematica Applicata e Tecnologie Informatiche     
Bertoluzza S., Canuto C., Tabacco A. Stable discretizations of convection-diffusion problems via computable negative-order inner products. Preprint ercim.cnr.ian//1999-1154, 1999.
 
 
Abstract
(English)
A new functional framework for consistently stabilizing discrete approximations to convection-diffusion problems was recently proposed by the authors. The key ideas are the evaluation of the residual in an inner product of type H^(-1/2) (unlike classical SUPG methods which use elemental weighted L^2-inner products), and the realization of this inner product via explicitely computable multilevel decompositions of function spaces (such as those given by wavelets or hierarchical finite elements). In the present paper, we first provide further motivations for our approach. Next we carry on a detailed analysis of the method, which covers all regimes (convection-dominated and diffusion-dominated). A consistent part of the analysis justifies the use of easily computable truncated forms of the stabilizing inner product. Numerical results, in close agreement with the theory, are given at the end of the paper.
Subject Singularly perturbed problems
Convection-diffusion problems
Stabilized Galerkin methods
Multiscale decompositions
Wavelets



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