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Augmented spaces, two‐level methods, and stabilizing subgrids
Author(s) -
Brezzi F.,
Marini L. D.
Publication year - 2002
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.265
Subject(s) - mathematics , stability (learning theory) , galerkin method , discontinuous galerkin method , residual , grid , mathematical optimization , computer science , mathematical analysis , finite element method , algorithm , geometry , physics , machine learning , thermodynamics
Abstract Starting from the already known relationship between stabilized methods, augmented spaces and residual‐free bubbles (RFB), the paper introduces a possible way of mimicking the effect of RFB just by constructing a suitable subgrid and then solving the standard Galerkin equations on the modified grid. Concentrating on the model problem of linear convection‐dominated equations, we give sufficient conditions on the subgrid that ensure stability, and error bounds of the same type of standard stabilizing procedures. Copyright © 2002 John Wiley & Sons, Ltd.