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Multilevel quadratic spline quasi-interpolation. (English) Zbl 1433.65017
Summary: In this paper, we present new approximation schemes based on both quasi-interpolation and multilevel methods by using bivariate quadratic B-spline functions, defined on simple and multiple knot type-2 triangulations, improving the classical quasi-interpolating spline results. We also prove polynomial reproduction, optimal approximation order and propose some numerical results and applications.
##### MSC:
 65D07 Numerical computation using splines 41A15 Spline approximation 41A25 Rate of convergence, degree of approximation 65D15 Algorithms for approximation of functions 41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX) 65D05 Numerical interpolation
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