The weighted essentially non-oscillatory {technique} using a stencil of 2r points (WENO-2r) is an interpolatory method that consists in obtaining a higher approximation order from the non-linear combination of interpolants of r+1 nodes. The result is an interpolant of order 2r at the smooth parts and order r+1 when an isolated discontinuity falls at any grid interval of the large stencil except at the central one. Recently, a new WENO method based on Aitken-Neville's algorithm has been designed for interpolation of equally spaced data at the mid-points and presents progressive order of accuracy close to discontinuities. This paper is devoted to constructing a general progressive WENO method for non-necessarily uniformly spaced data and several variables interpolating in any point of the central interval. Also, we provide explicit formulas for linear and non-linear weights and prove the order obtained. Finally, some numerical experiments are presented to check the theoretical results.
@article{arxiv.2404.16694,
title = {A non-separable progressive multivariate WENO-$2r$ point value},
author = {Pep Mulet and Juan Ruiz-Alvarez and Chi-Wang Shu and Dionisio F. Yáñez},
journal= {arXiv preprint arXiv:2404.16694},
year = {2024}
}