A non-separable progressive multivariate WENO-2r point value

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2024-06-07 DOI:10.1016/j.apnum.2024.05.025

Pep Mulet , Juan Ruiz-Álvarez , Chi-Wang Shu , Dionisio F. Yáñez

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引用次数: 0

Abstract

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.

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不可分割的渐进多元 WENO-2r 点值

使用 2r 点钢网的加权基本非振荡技术（WENO-2r）是一种内插方法，它包括从 r+1 个节点的内插值的非线性组合中获得更高的近似阶数。其结果是，在平滑部分的插值阶数为 2r，而当孤立的不连续性落在大模板的任何网格间隔（中心间隔除外）时，插值阶数为 r+1。最近，基于 Aitken-Neville 算法设计了一种新的 WENO 方法，用于等间距数据的中点插值，并在接近不连续点时呈现逐步提高的精度阶次。本文致力于构建一种通用的渐进式 WENO 方法，该方法适用于在中心区间的任意点进行插值的非等距数据和多个变量。此外，我们还提供了线性和非线性权重的明确公式，并证明了所获得的阶次。最后，我们给出了一些数值实验来检验理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.