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Mathematics of Computation

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


Author: Edward J. Fuselier
Journal: Math. Comp. 77 (2008), 1407-1423
MSC (2000): Primary 41A63, 41A05; Secondary 41A30, 65D05
DOI: https://doi.org/10.1090/S0025-5718-07-02096-0
Published electronically: December 27, 2007
MathSciNet review: 2398774
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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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Additional Information

Edward J. Fuselier
Affiliation: Department of Mathematical Sciences, United States Military Academy, West Point, New York 10996
Email: edward.fuselier@usma.edu

DOI: https://doi.org/10.1090/S0025-5718-07-02096-0
Received by editor(s): June 5, 2006
Received by editor(s) in revised form: April 8, 2007
Published electronically: December 27, 2007
Additional Notes: The results are part of the author’s dissertation written under the guidance of Francis Narcowich and Joe Ward at Texas A&M University, College Station, Texas 77843