Error estimates for interpolating div-curl splines under tension on a bounded domain (Q927691)

The theory of radial basis function interpolation and its variational aspects is well developed. In this paper, the aspect of tension parameters in the radial basis functions is of particular relevance. The authors use the variational property with respect to semi-norms combined from div and curl and call the resulting minimizing splines `div-curl splines'. Their existence, the spaces where they are defined, and their convergence properties are studied in detail. The underlying domains for approximand and approximant are bounded and Lipschitz. The tension parameter which is used comes from the aforementioned linear combination of semi-norms.