Constructing Good Coefficient Functionals for Bivariate C~1 Quadratic Spline Quasi-Interpolants

摘要

We consider discrete quasi-interpolants based on C~1 quadratic box-splines on uniform criss-cross triangulations of a rectangular domain.The main problem consists in finding good (if not best) coefficient functionals, associated with boundary box-splines, giving both an optimal approximation order and a small infinity norm of the operator.Moreover, we want that these functionals only involve data points inside the domain.They are obtained either by minimizing their infinity norm w.r.t.a finite number of free parameters, or by inducing superconvergence of the operator at some specific points lying near or on the boundary.