On the approximation order of splines on spherical triangulations
The standard splines on Euclidean spaces are piecewise algebraic polynomials on triangulations (in two dimensions) or on other partitions in higher dimensions. Polynomials on spheres which are suitable to approximation functions defined there are usually homogeneous polynomials, restricted to spheres. Additional smoothness conditions are added in all cases so that the splines are in \(C^r\), say. In this paper, approximations of this kind on spheres are carefully analysed with a special emphasis on their approximation (convergence) orders. Lower bounds on the approximation orders are provided where seminorms of the approximands appear in the bounds whose order is related to the polynomial degree of the spline.
scientific article; zbMATH DE number 2069016