Abstract A general framework for proving error bounds and convergence of a large class of unsymmetric meshless numerical methods for
solving well-posed linear operator equations is presented. The results provide optimal convergence rates, if the test and
trial spaces satisfy a stability condition. Operators need not be elliptic, and the problems can be posed in weak or strong
form without changing the theory. Non-stationary kernel-based trial and test spaces are shown to fit into the framework, disregarding
the operator equation. As a special case, unsymmetric meshless kernel-based methods solving weakly posed problems with distributional
data are treated in some detail. This provides a foundation of certain variations of the “Meshless Local Petrov-Galerkin”
technique of S.N. Atluri and collaborators.
solving well-posed linear operator equations is presented. The results provide optimal convergence rates, if the test and
trial spaces satisfy a stability condition. Operators need not be elliptic, and the problems can be posed in weak or strong
form without changing the theory. Non-stationary kernel-based trial and test spaces are shown to fit into the framework, disregarding
the operator equation. As a special case, unsymmetric meshless kernel-based methods solving weakly posed problems with distributional
data are treated in some detail. This provides a foundation of certain variations of the “Meshless Local Petrov-Galerkin”
technique of S.N. Atluri and collaborators.
- Content Type Journal Article
- DOI 10.1007/s00211-009-0265-z
- Authors
- Robert Schaback, Universität Göttingen Institut für Numerische und Angewandte Mathematik Lotzestrasse 16-18 37083 Göttingen Germany
- Journal Numerische Mathematik
- Online ISSN 0945-3245
- Print ISSN 0029-599X
