In this article we present a generalization of the WENO algorithm of order six for data discretized in the point values introduced in Amat et al. (2019). This generalization requires a slight modification of the mentioned algorithm. The objective is to obtain a new WENO algorithm of order $2r$ that is capable of rising the accuracy of the interpolation step by step close to the discontinuities. In order to keep the computational cost controlled, we will propose simple smoothness indicators of high order as a function of those used by the classical implementation of WENO. We will discuss about the accuracy of the new algorithm and present numerical experiments that support our claims.

在本文中，我们介绍了针对Amat等人介绍的点值离散化的数据的六阶WENO算法的一般化。（2019）。这种概括要求对所提到的算法进行一些修改。目的是获得一种新的阶的WENO算法$2\mathrm{[R}$能够逐步提高接近不连续点的插值精度。为了使计算成本得到控制，我们将提出简单的高阶平滑度指标，作为WENO的经典实现所使用的指标的函数。我们将讨论新算法的准确性，并提供支持我们主张的数值实验。