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Subgrid stabilization of Galerkin approximations of monotone operators
Author(s) -
Guermond J.L.
Publication year - 1999
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19990791308
Subject(s) - galerkin method , monotone polygon , hilbert space , mathematics , bilinear interpolation , bilinear form , approximations of π , space (punctuation) , diffusion , mathematical analysis , discontinuous galerkin method , nonlinear system , computer science , physics , finite element method , geometry , quantum mechanics , statistics , thermodynamics , operating system
This paper presents a stabilized Galerkin technique for approximating monotone linear operators in a Hilbert space. The key idea consists an introducing an approximation space that is broken up into large scales and small scales so that the bilinear form associated with the problem satisfies a uniform inf‐sup condition with respect to this decomposition. An optimal Galerkin approximation is obtained by introducing an artificial diffusion on the small scales.