SUPG stabilization of meshfree methods for convection‐dominated problems

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.