• Corpus ID: 239998699

Stability estimates for radial basis function methods applied to time-dependent hyperbolic PDEs

@article{Tominec2021StabilityEF,
  title={Stability estimates for radial basis function methods applied to time-dependent hyperbolic PDEs},
  author={Igor Tominec and Murtazo Nazarov and Elisabeth Larsson},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.14548}
}
We derive stability estimates for three commonly used radial basis function (RBF) methods to solve hyperbolic time-dependent PDEs: the RBF generated finite difference (RBF-FD) method, the RBF partition of unity method (RBF-PUM) and Kansa’s (global) RBF method. We give the estimates in the discrete `2-norm intrinsic to each of the three methods. The results show that Kansa’s method and RBF-PUM can be `2-stable in time under a sufficiently large oversampling of the discretized system of equations… 

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