On new strategies to control the accuracy of WENO algorithms close to discontinuities
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The work of the authors was supported by the Programa de Apoyo a la Investigatión de la Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia 20928/PI/18, by the national research project MTM2015-64382-P (MINECO/FEDER), and by National Science Foundation grant DMS-1719410.Fecha de publicación
2019Editorial
Society for Industrial and Applied MathematicsCita bibliográfica
Amat, S., Ruiz, J., & Shu, C. (2019). On New Strategies to Control the Accuracy of WENO Algorithms Close to Discontinuities. SIAM Journal on Numerical Analysis, 57(3), 1205–1237. doi:10.1137/18m1214937Palabras clave
WENO schemesNew optimal weights
Improved adaption to discontinuities
Signal processing
Resumen
This paper is devoted to the construction and analysis of new nonlinear optimal weights for weighted ENO (WENO) interpolation capable of raising the order of accuracy close to discontinuities. The new nonlinear optimal weights are constructed using a strategy inspired by the original WENO algorithm, and they work very well for corner or jump singularities, leading to optimal theoretical accuracy. This is the first part of a series of two papers. In this first part we analyze the performance of the new algorithms proposed for univariate function approximation in the point values (interpolation problem). In the second part, we will extend the analysis to univariate function approximation in the cell averages (reconstruction problem). Our aim is twofold: to raise the order of accuracy of the WENO type interpolation schemes both near discontinuities and in the interval which contains the singularity. The first problem can be solved using the new nonlinear optimal weights, but the second one ...
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