# A Smoothness Indicator for Adaptive Algorithms for Hyperbolic Systems

@article{Karni2002ASI, title={A Smoothness Indicator for Adaptive Algorithms for Hyperbolic Systems}, author={Smadar Karni and Alexander Kurganov and Guergana Petrova}, journal={Journal of Computational Physics}, year={2002}, volume={178}, pages={323-341} }

The formation of shock waves in solutions of hyperbolic conservation laws calls for locally adaptive numerical solution algorithms and requires a practical tool for identifying where adaption is needed. In this paper, a new smoothness indicator (SI) is used to identify “rough” solution regions and is implemented in locally adaptive algorithms. The SI is based on the weak local truncation error of the approximate solution. It was recently reported in S. Karni and A. Kurganov, Local error…

## 58 Citations

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- 2007

It is shown that, even though the MAPR is not designed with the goal of obtaining a scheme that satisfies a maximum principle or is total-variation diminishing (TVD) in mind, it provides a robust nonoscillatory reconstruction that captures composite waves accurately.

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This paper develops cubic and quintic B-spline quasi-interpolation based numerical methods for hyperbolic conservation laws in 1 space dimension, and shows that they achieve the rate of convergence 4 and 6.

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- 2011

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