Error estimates for reconstruction using thin plate spline interpolants

Abstract

Using thin plate spline interpolants we derive error bounds for the reconstruction of point values where the interpolation data is given by cell values. Sonar investigates in [IMA J. of Num. Analysis 16, 1996, 549-581] numerical solutions of hyperbolic conservation laws where the local reconstruction step is performed using thin plate spline interpolants. We show that local reconstruction yields second order as in the global case but without assuming additional boundary conditions and smoothness requirements.