Numerical integration based on quasi-interpolating splines

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

“…Legendre product [13] product [19] rule [19] Such examples show that the choice of the partition can be crucial for the accuracy of the results.…”

“…This is an advantage with respect to other known ones [13,27,38], always based on B-splines, that need also function evaluation points outside Ω .…”

“…We remark that the proposed schemes could be used in the numerical evaluation of 2D singular integrals, defined in the Hadamard finite part sense [12,13].…”

“…In tables 4.1, 4.2, 4.3 we present the relative errors provided by the application of our rules on uniform criss-cross triangulations and other known ones, given in [13,27] and [19], p.216, in particular Simpson product rule, with approximation order O(∆ 4 ), and the ones based on the Schoenberg-Marsden operators S u and S nu , defined by using simple knot B-splines on uniform and nonuniform criss-cross triangulations, respectively, whose approximation order is the same as the integration rule based on S 1 .…”

“…Based on this QI, cubature formulas have been generated in [12,13], also for finite part integrals. These results have been generalized to nonuniform crisscross triangulations T mn of Ω in [27,38].…”