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Non‐local and semi‐local optimal weighting functions for symmetric problems involving a small parameter
Author(s) -
Givoli Dan
Publication year - 1988
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620260605
Subject(s) - weighting , quantum nonlocality , mathematics , galerkin method , norm (philosophy) , petrov–galerkin method , perturbation (astronomy) , mathematical optimization , mathematical analysis , finite element method , physics , quantum mechanics , quantum entanglement , acoustics , political science , law , quantum , thermodynamics
The method of optimal weighting functions for symmetric problems is described in a general form. It is based on a Petrov‐Galerkin formulation in which the best approximation property and other mathematical features are achieved for a chosen norm, different from the original ‘energy norm’ of the problem. The nonlocality of the weighting functions is shown to have only a minor effect on the efficiency of the method, although a localization scheme is also suggested. The method is applied to a one‐ and two‐dimensional singular perturbation problems, as well as to a cylindrical shell problem.