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Stability of semi-Lagrangian schemes of arbitrary odd degree under constant and variable advection speed. (English) Zbl 1436.65137

Summary: The equivalence between semi-Lagrangian and Lagrange-Galerkin schemes has been proved by the first author [J. Comput. Math. 28, No. 4, 461–473 (2010; Zbl 1240.65290); Numer. Math. 124, No. 1, 31–56 (2013; Zbl 1268.65135)] for the case of centered Lagrange interpolation of odd degree \(p\leq 13\). 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.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
65D07 Numerical computation using splines

Software:

Matlab; DLMF
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Full Text: DOI

References:

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