Error bounds for minimal energy bivariate polynomial splines
This paper is on bivariate splines that are used to approximate function values at scattered points. The bivariate polynomial splines are chosen by interpolation , i.e. they must meet prescribed function values at given points, and so as to minimize an energy semi-norm. This semi-norm is defined through second derivatives and therefore has linear polynomials in its null-space. The main result gives error bounds on such minimal energy interpolants, provided we interpolate from a bivariate spline space with a suitable stable local basis and the splines are formed by a quasi-uniform triangulation.
scientific article; zbMATH DE number 1884031