Smoothness indicators for WENO scheme using undivided differences

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Tamer H. M. A. Kasem Francois Schmitt


The weighted essentially non-oscillatory method (WENO) has been used widely in numerical solutions during the last two decades. This method relies on Smoothness Indicators (SI) to produce smooth solutions near discontinuities. It was concluded before that evaluating SI based on undivided differences (UD) is inefficient, and the $L2$ norm of the interpolation polynomials was used instead. In the current study the idea of using UD is revisited with the key feature of careful selection of the stencil. Improvement in terms of the accuracy and the number of arithmetic operations is illustrated by numerical simulations.

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KASEM, Tamer H. M. A.; SCHMITT, Francois. Smoothness indicators for WENO scheme using undivided differences. Proceedings of the Conference Algoritmy, [S.l.], p. 155-164, feb. 2016. Available at: <>. Date accessed: 22 sep. 2017.


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