Vector field approximation using radial basis functions

In this article, we investigate the performance of RBF–PDE methods for approximating solenoidal fields. It is well known that global RBF collocation methods present a trade-off principle, which means that smoothness implies high convergence order plus ill-conditioning. On the other hand, local methods for solving this problem have recently appeared in the literature. In this paper, we perform a numerical investigation of the differences between RBF global and local methods, in order to investigate the possible advantage of using local methods for the approximation of vector fields. More precisely, we compare the local Hermite interpolation technique using inverse multiquadrics against the non-symmetric collocation method of Kansa.