Entropy stable essentially nonoscillatory methods based on RBF reconstruction
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 3, pp. 925-958.

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.

DOI : 10.1051/m2an/2019011
Classification : 35L65, 65M12, 65M06, 65M08, 65D05
Mots-clés : Radial basis functions, entropy stability, sign-property, finite differences, finite volume methods, high-order accuracy, ENO reconstruction
Hesthaven, Jan S. 1 ; Mönkeberg, Fabian 1

1 
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     title = {Entropy stable essentially nonoscillatory methods based on {RBF} reconstruction},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {925--958},
     publisher = {EDP-Sciences},
     volume = {53},
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     year = {2019},
     doi = {10.1051/m2an/2019011},
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     url = {http://www.numdam.org/articles/10.1051/m2an/2019011/}
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Hesthaven, Jan S.; Mönkeberg, Fabian. Entropy stable essentially nonoscillatory methods based on RBF reconstruction. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 3, pp. 925-958. doi : 10.1051/m2an/2019011. http://www.numdam.org/articles/10.1051/m2an/2019011/

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