Nonlinear 2D C1 Quadratic Spline Quasi-Interpolants on Triangulations for the Approximation of Piecewise Smooth Functions Article Swipe

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Classification of discontinuities Spline (mechanical) Piecewise Quadratic equation Mathematics Nonlinear system Bivariate analysis Gibbs phenomenon Applied mathematics Mathematical analysis Convergence (economics) Geometry Physics Quantum mechanics Fourier transform Economic growth Statistics Thermodynamics Economics

Francesc Aràndiga , Sara Remogna ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.3390/axioms12101002 · OA: W4387874098

The aim of this paper is to present and study nonlinear bivariate C1 quadratic spline quasi-interpolants on uniform criss-cross triangulations for the approximation of piecewise smooth functions. Indeed, by using classical spline quasi-interpolants, the Gibbs phenomenon appears when approximating near discontinuities. Here, we use weighted essentially non-oscillatory techniques to modify classical quasi-interpolants in order to avoid oscillations near discontinuities and maintain high-order accuracy in smooth regions. We study the convergence properties of the proposed quasi-interpolants and we provide some numerical and graphical tests confirming the theoretical results.