In this paper, we investigate the application of radial basis functions (RBFs) for the approximation with collocation of the Stokes problem. The approximate solution is constructed in a multi-level fashion, each level using compactly supported radial basis functions with decreasing scaling factors. We use symmetric collocation and give sufficient conditions for convergence and consider stability analysis. Numerical experiments support the theoretical results.
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Communicated by: Robert Schaback
This work was supported by the Australian Research Council.
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Chernih, A., Le Gia, Q.T. Multiscale methods with compactly supported radial basis functions for the Stokes problem on bounded domains. Adv Comput Math 42, 1187–1208 (2016). https://doi.org/10.1007/s10444-016-9458-z