Abstract
Quasi-interpolation based on B-spline approximation methods are used in numerous applications. However, we observe that the Gibbs phenomenon appears when approximating near discontinuities. We present nonlinear modifications, based on weighted essentially non-oscillatory (WENO) techniques, of well-known quasi-interpolation methods to avoid this phenomena near discontinuities and, at the same time, maintain the high-order accuracy in smooth regions.
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