Abstract
We show how one may interpolate a vector-valued function in two or three dimensions, whose value is (wholly or partly) known at a sufficient (but not large) number of points disposed in almost any configuration, under the condition that the interpolating function has zero divergence. The technique is based on the theory of thin-plate splines. One may use a similar scheme in the case where the data consist of flux integrals (or other linear functionals) of the unknown function.
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References
P.J. Davis,Interpolation and Approximation (Blaisdell, 1963).
J. Duchon, Interpolation des fonctions de deux variables, suivant le principe de la flexion des plaques minces, RAIRO Numer. Anal. 10 (1976) 5–12.
D.C. Handscomb, Interpolation and differentiation of multivariate functions and interpolation of divergence-free vector fields using surface splines, Report 91/5, Oxford University Computing Laboratory, Numerical Analysis Group, 11 Keble Road, Oxford OX1 3QD (1991).
J. Meinguet, Multivariate interpolation at arbitrary points made simple, Z. Angew. Math. Phys. 30 (1979) 292–304.
J. Meinguet, Surface spline interpolation: basic theory and computational aspects, in:Approximation Theory and Spline Functions, eds. S.P. Singh et al. (Reidel, 1984) pp. 127–142.
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Handscomb, D. Local recovery of a solenoidal vector field by an extension of the thin-plate spline technique. Numer Algor 5, 121–129 (1993). https://doi.org/10.1007/BF02212043
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DOI: https://doi.org/10.1007/BF02212043