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

Ferretti, Roberto; Mehrenberger, Michel

doi:10.1090/mcom/3494

Stability of semi-Lagrangian schemes of arbitrary odd degree under constant and variable advection speed
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by Roberto Ferretti and Michel Mehrenberger;

Math. Comp. 89 (2020), 1783-1805

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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