A least squares radial basis function finite difference method with improved stability properties
Numerical Analysis
2021-03-16 v2 Numerical Analysis
Abstract
Localized collocation methods based on radial basis functions (RBFs) for elliptic problems appear to be non-robust in the presence of Neumann boundary conditions. In this paper we overcome this issue by formulating the RBF-generated finite difference method in a discrete least-squares setting instead. This allows us to prove high-order convergence under node refinement and to numerically verify that the least-squares formulation is more accurate and robust than the collocation formulation. The implementation effort for the modified algorithm is comparable to that for the collocation method.
Cite
@article{arxiv.2003.03132,
title = {A least squares radial basis function finite difference method with improved stability properties},
author = {Igor Tominec and Elisabeth Larsson and Alfa Heryudono},
journal= {arXiv preprint arXiv:2003.03132},
year = {2021}
}