Sobolev-type approximation rates for divergence-free and curl-free RBF interpolants

Fuselier, Edward

doi:10.1090/S0025-5718-07-02096-0

Sobolev-type approximation rates for divergence-free and curl-free RBF interpolants
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by Edward J. Fuselier;

Math. Comp. 77 (2008), 1407-1423

DOI: https://doi.org/10.1090/S0025-5718-07-02096-0

Published electronically: December 27, 2007

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Abstract:

Recently, error estimates have been made available for divergence-free radial basis function (RBF) interpolants. However, these results are only valid for functions within the associated reproducing kernel Hilbert space (RKHS) of the matrix-valued RBF. Functions within the associated RKHS, also known as the “native space” of the RBF, can be characterized as vector fields having a specific smoothness, making the native space quite small. In this paper we develop Sobolev-type error estimates when the target function is less smooth than functions in the native space.

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