Some performances of local bivariate quadratic C1 quasi-interpolating splines on nonuniform type-2 triangulations

Numerical integration based on bivariate quadratic spline quasi-interpolants on bounded domains

“…In [7,8] some approximation power performances and error analysis on the function and on its partial derivatives of first and second order with local and global upper bounds are given for such a general class of spline QIs.…”

On the construction of local quadratic spline quasi-interpolants on bounded rectangular domains

“…Given in input the knots, defined by (1) with the choice (3), the matrix {λ i j f } defined by (5) and an arbitrary grid u × v of evaluation points in , the procedure returns the values of the bivariate spline Q f at u × v, according to (6). It calls bijdec.…”

“…Finally it has been shown [6] that they can be directly used to provide splines with boundary conditions. We recall that similar operators, based on "classical" B-splines [3], have been defined and studied in the literature [4,5,17]. However they haven't the performances of the ones above; for instance they need function evaluation points also outside and they cannot be directly used for boundary condition splines.…”

On the Approximation of the Derivatives of Spline Quasi-Interpolation in Cubic Spline $S_3^{1,2}(∆_{mn}^{(2)})$

“…These spline quasi-interpolating operators can reproduce any polynomial of (nearly) best degrees, respectively. Moreover, spline quasiinterpolation defined by discrete linear functionals based on a fixed number of triangular mesh-points has been investigated, which showed that they could approximate a real function and its partial derivatives up to an optimal order in [1,2].…”