Approximation of piecewise smooth functions by nonlinear bivariate \(C^2\) quartic spline quasi-interpolants on criss-cross triangulations (Q6577605)

The authors focus on the space of \(C^2\) quartic splines on uniform criss-cross triangulations and propose a method based on weighted essentially non-oscillatory techniques and obtained by modifying classical spline quasi-interpolants in order to approximate piecewise smooth functions avoiding Gibbs phenomenon near discontinuities and, at the same time, maintaining the high order accuracy in smooth regions.