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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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