Generalized Hermite interpolation via matrix-valued conditionally positive definite functions
Mathematics of Computation
Continuous and discrete least-squares approximation by radial basis functions on spheres
Journal of Approximation Theory
Meshless Collocation: Error Estimates with Application to Dynamical Systems
SIAM Journal on Numerical Analysis
Divergence-Free Kernel Methods for Approximating the Stokes Problem
SIAM Journal on Numerical Analysis
Approximation in rough native spaces by shifts of smooth kernels on spheres
Journal of Approximation Theory
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Recently [D. Schräder and H. Wendland, Math. Comp., 80 (2011), pp. 263-277], a new meshfree approximation method for Darcy's problem has been introduced and analyzed. This method is based on a symmetric collocation approach using radial basis functions producing solutions with an analytically divergence-free velocity part. However, the error analysis provided in that paper works only for smooth solutions, where the smoothness is intrinsically linked to the smoothness of the employed basis function. In this paper, we will extend the error analysis to less smooth functions, showing that the approximation order for rougher solutions is determined by the smoothness of the solution rather than the smoothness of the basis function.