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Stability of Semi-Lagrangian schemes of arbitrary odd degree under constant and variable advection speed


Authors: Roberto Ferretti and Michel Mehrenberger
Journal: Math. Comp. 89 (2020), 1783-1805
MSC (2010): Primary 65M12, 65M50, 65M25
DOI: https://doi.org/10.1090/mcom/3494
Published electronically: December 16, 2019
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Abstract: The equivalence between semi-Lagrangian and Lagrange-Galerkin schemes has been proved by R. Ferretti [J. Comp. Math. 28 (2010), no. 4, 461-473], [Numerische Mathematik 124 (2012), no. 1, 31-56] for the case of centered Lagrange interpolation of odd degree $ p\le 13$. We generalize this result to an arbitrary odd degree, for both the case of constant- and variable-coefficient equations. In addition, we prove that the same holds for spline interpolations.


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Additional Information

Roberto Ferretti
Affiliation: Dipartimento di Matematica e Fisica, Università Roma Tre, Roma, Italy
Email: ferretti@mat.uniroma3.it

Michel Mehrenberger
Affiliation: Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France
Email: michel.mehrenberger@univ-amu.fr

DOI: https://doi.org/10.1090/mcom/3494
Received by editor(s): July 23, 2018
Received by editor(s) in revised form: February 13, 2019, July 2, 2019, and October 1, 2019
Published electronically: December 16, 2019
Additional Notes: The first author has been partially supported by IRMA Strasbourg and INdAM–GNCS project “Metodi numerici per equazioni iperboliche e cinetiche e applicazioni”.
This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under grant agreement No 633053.
Article copyright: © Copyright 2019 American Mathematical Society