Stability estimates for radial basis function methods applied to linear scalar conservation laws

Igor Tominec, Murtazo Nazarov and Elisabeth Larsson

Applied Mathematics and Computation, 2025, vol. 485, issue C

Abstract: 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 ℓ2-norm intrinsic to each of the three methods. The results show that Kansa's method and RBF-PUM can be ℓ2-stable in time under a sufficiently large oversampling of the discretized system of equations. The RBF-FD method in addition requires stabilization of the spurious jump terms due to the discontinuous RBF-FD cardinal basis functions. Numerical experiments show an agreement with our theoretical observations.

Keywords: Radial basis function; Stability; Hyperbolic PDE; Kansa; RBF-PUM; RBF-FD (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:485:y:2025:i:c:s0096300324004818

DOI: 10.1016/j.amc.2024.129020

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