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SUPG stabilization of meshfree methods for convection‐dominated problems
Author(s) -
Fries ThomasPeter,
Matthies Hermann G.
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310462
Subject(s) - meshfree methods , kronecker delta , property (philosophy) , mathematics , computer science , mathematical optimization , convection , galerkin method , finite element method , mechanics , structural engineering , physics , engineering , philosophy , epistemology , quantum mechanics
Streamline‐Upwind/Petrov‐Galerkin (SUPG) stabilization of meshfree methods with stabilization parameters calculated from standard formulas, which have their roots in mesh‐based methods, often leads to unsatisfactory results. A new procedure for obtaining adequate SUPG stabilization parameters for meshfree methods is presented. It is shown that the Kronecker‐δ property is very advantageous for a successful stabilization because this leads to local stabilization criteria. If the meshfree shape functions lack this property, a stabilization based on local properties – i.e. on nodes in the neighbourhood – cannot be sufficient for highly convection‐dominated problems.