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Old   April 23, 2004, 07:09
Default Stabilization techniques?
Mihail Galabov
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Hi everyone, Could someone tell me anything about stabilization techniques like Stramline Diffusion(Hiughes,Franca,Johnson) or Characteristics Method (Pironneau) or some else and where I can find these books/publications?

Thank's in advance, Mihail
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Old   April 23, 2004, 11:57
Default Re: Stabilization techniques?
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Stabilization Methods in FEM:

SUPG method was proposed by Hughes and Brooks (1982 Computer methods in applied mechanics and engineering). Then GLS method was proposed by Hughes. The idea is simple. Add some stabilzation terms in addition to standard Galerkin terms. These formulations give optimal convergence for equal order interpolation function for pressure and velocity (in the contest of incompressible NS). Franca worked on the mathematical aspects of determination of stabilization parameter. Tyfun Tezduyar's work is mainly on performing numerical testings and determining correct "Tau"

Recently a new approach is introduced which is called Multiscale stabilization. This approach is based on the notion of multiple scale solutions (coarse-resolved and fine-unresolved). Stabilization comes automatically and you dont have to design and predefined stabilization parameter. Look into the following reference for details. I will be more than happy to answers any firther questions

A.Masud, R.A. Khurram "A multiscale/stabilized finite element method for the advection–diffusion equation",Comput. Methods Appl. Mech. Engrg. 193 (2004), pp. 1997-2018

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