### ON NEW STRATEGIES TO CONTROL THE ACCURACY OF WENO ALGORITHM CLOSE TO DISCONTINUITIES II: CELL AVERAGES AND MULTIRESOLUTION

Sergio Amat1, Juan Ruiz1, Chi-Wang Shu2

1. 1. Department of Applied Mathematics and Statistics, Universidad Politécnica de Cartagena, Spain;
2. Division of Applied Mathematics, Brown University, USA
• Received:2019-05-20 Revised:2020-02-19 Online:2020-07-15 Published:2020-07-15
• Supported by:

The first and second authors have been supported through project 20928/PI/18 (Proyecto financiado por la Comunidad Autónoma de la Región de Murcia a través de la convocatoria de Ayudas a proyectos para el desarrollo de investigación científica y técnica por grupos competitivos, incluida en el Programa Regional de Fomento de la Investigación Científica y Técnica (Plan de Actuación 2018) de la Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia) and by the national research project MTM2015-64382-P (MINECO/FEDER). The third author has been supported through the National Science Foundation grant DMS-1719410.

Sergio Amat, Juan Ruiz, Chi-Wang Shu. ON NEW STRATEGIES TO CONTROL THE ACCURACY OF WENO ALGORITHM CLOSE TO DISCONTINUITIES II: CELL AVERAGES AND MULTIRESOLUTION[J]. Journal of Computational Mathematics, 2020, 38(4): 661-682.

This paper is the second part of the article and is devoted to the construction and analysis of new non-linear optimal weights for WENO interpolation capable of rising the order of accuracy close to discontinuities for data discretized in the cell averages. Thus, now we are interested in analyze the capabilities of the new algorithm when working with functions belonging to the subspace L1L2 and that, consequently, are piecewise smooth and can present jump discontinuities. The new non-linear optimal weights are redesigned in a way that leads to optimal theoretical accuracy close to the discontinuities and at smooth zones. We will present the new algorithm for the approximation case and we will analyze its accuracy. Then we will explain how to use the new algorithm in multiresolution applications for univariate and bivariate functions. The numerical results confirm the theoretical proofs presented.

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