Volume 38, Issue 4
On New Strategies to Control the Accuracy of WENO Algorithm Close to Discontinuities II: Cell Averages and Multiresolution

J. Comp. Math., 38 (2020), pp. 661-682.

Published online: 2020-05

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• Abstract

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 $L^1\cap L^2$ 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.

• Keywords

WENO, Cell averages, New optimal weights, Multiresolution schemes, Improved adaption to discontinuities, Signal processing.

65D05, 65D17, 65M06, 65N06

sergio.amat@upct.es (Sergio Amat )

juan.ruiz@upct.es (Juan Ruiz )

Chi-Wang_Shu@brown.edu (Chi-Wang Shu )

• BibTex
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• TXT
@Article{JCM-38-661, author = {Amat , Sergio and Ruiz , Juan and Shu , Chi-Wang }, title = {On New Strategies to Control the Accuracy of WENO Algorithm Close to Discontinuities II: Cell Averages and Multiresolution}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {4}, pages = {661--682}, abstract = {

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 $L^1\cap L^2$ 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1903-m2019-0125}, url = {http://global-sci.org/intro/article_detail/jcm/16859.html} }
TY - JOUR T1 - On New Strategies to Control the Accuracy of WENO Algorithm Close to Discontinuities II: Cell Averages and Multiresolution AU - Amat , Sergio AU - Ruiz , Juan AU - Shu , Chi-Wang JO - Journal of Computational Mathematics VL - 4 SP - 661 EP - 682 PY - 2020 DA - 2020/05 SN - 38 DO - http://doi.org/10.4208/jcm.1903-m2019-0125 UR - https://global-sci.org/intro/article_detail/jcm/16859.html KW - WENO, Cell averages, New optimal weights, Multiresolution schemes, Improved adaption to discontinuities, Signal processing. AB -

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 $L^1\cap L^2$ 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.

Sergio Amat , Juan Ruiz & Chi-Wang Shu . (2020). On New Strategies to Control the Accuracy of WENO Algorithm Close to Discontinuities II: Cell Averages and Multiresolution. Journal of Computational Mathematics. 38 (4). 661-682. doi:10.4208/jcm.1903-m2019-0125
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