Axioms (Oct 2023)

Nonlinear 2D <i>C</i><sup>1</sup> Quadratic Spline Quasi-Interpolants on Triangulations for the Approximation of Piecewise Smooth Functions

  • Francesc Aràndiga,
  • Sara Remogna

DOI
https://doi.org/10.3390/axioms12101002
Journal volume & issue
Vol. 12, no. 10
p. 1002

Abstract

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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.

Keywords