Volume 53, Number 3, May-June 2019
|Page(s)||925 - 958|
|Published online||21 June 2019|
Entropy stable essentially nonoscillatory methods based on RBF reconstruction
SB-MATHICSE-MCSS, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland
* Corresponding author: firstname.lastname@example.org
Accepted: 11 February 2019
To solve hyperbolic conservation laws we propose to use high-order essentially nonoscillatory methods based on radial basis functions. We introduce an entropy stable arbitrary high-order finite difference method (RBF-TeCNOp) and an entropy stable second order finite volume method (RBF-EFV2) for one-dimensional problems. Thus, we show that methods based on radial basis functions are as powerful as methods based on polynomial reconstruction. The main contribution is the construction of an algorithm and a smoothness indicator that ensures an interpolation function which fulfills the sign-property on general one dimensional grids.
Mathematics Subject Classification: 35L65 / 65M12 / 65M06 / 65M08 / 65D05
Key words: Radial basis functions / entropy stability / sign-property / finite differences / finite volume methods / high-order accuracy / ENO reconstruction
© The authors. Published by EDP Sciences, SMAI 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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