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

https://doi.org/10.1016/j.apnum.2024.05.025

Mulet, Pep; Ruiz-Álvarez, Juan; Shu, Chi-Wang; Yáñez, Dionisio F (October 2024, Applied Numerical Mathematics)

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On the approximation of derivative values using a WENO algorithm with progressive order of accuracy close to discontinuities

https://doi.org/10.1007/s40314-022-02004-z

Amat, Sergio; Ruiz-Álvarez, Juan; Shu, Chi-Wang; Yáñez, Dionisio F. (September 2022, Computational and Applied Mathematics)

Abstract In this article, we introduce a new WENO algorithm that aims to calculate an approximation to derivative values of a function in a non-regular grid. We adapt the ideas presented in [Amat et al., SIAM J. Numer. Anal. (2020)] to design the nonlinear weights in a manner such that the order of accuracy is maximum in the intervals close to the discontinuities. Some proofs, remarks on the choice of the stencils and explicit formulas for the weights and smoothness indicators are given. We also present some numerical experiments to confirm the theoretical results.
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Cell-average WENO with progressive order of accuracy close to discontinuities with applications to signal processing

https://doi.org/10.1016/j.amc.2021.126131

Amat, Sergio; Ruiz-Álvarez, Juan; Shu, Chi-Wang; Yáñez, Dionisio F. (August 2021, Applied Mathematics and Computation)
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