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

Author

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  • Tominec, Igor
  • Nazarov, Murtazo
  • Larsson, Elisabeth

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.

Suggested Citation

  • Tominec, Igor & Nazarov, Murtazo & Larsson, Elisabeth, 2025. "Stability estimates for radial basis function methods applied to linear scalar conservation laws," Applied Mathematics and Computation, Elsevier, vol. 485(C).
    • Handle: RePEc:eee:apmaco:v:485:y:2025:i:c:s0096300324004818
    DOI: 10.1016/j.amc.2024.129020
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