One dimensional hybrid WENO-AO method using improved troubled cell indicator based on extreme point

One dimensional troubled cell indicator, which is based on the extreme point of approximated polynomial, was proposed by Zhu and Qiu (SIAM J. Sci. Comput. 39:A1089-A1113, 2017). This troubled cell indicator performs well, but still has two shortcomings. First, it calculates the extreme point of highdegree polynomial, however the calculation is not simple. The reason is that, the explicit formula of extreme point of quartic polynomial has been complex, the one of higher degree polynomial becomes more complex or even is hard to be obtained, so has to be calculated by using numerical method. Second, a complex or without explicit formula of extreme point will bring tremendous difficulty to analyze why the troubled cell indicator can capture the major character of solution. In order to overcome these shortcomings, we first improve the troubled cell indicator, then use it to design the hybrid WENO-AO method for solving one dimensional hyperbolic conservation laws. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

The one dimensional troubled cell indicator, based on extreme points of approximated polynomials, proposed by Zhu and Qiu in 2017, performs well but has two main drawbacks. Firstly, calculating extreme points of high degree polynomials is complex. Secondly, the complexity of extreme points makes it difficult to analyze how the indicator captures the main characteristics of the solution.