Following a previous result stating their equivalence under constant advection speed, Semi-Lagrangian and Lagrange-Galerkin schemes are compared in this paper in the situation of variable coefficient advection equations. Once known that Semi-Lagrangian schemes can be proved to be equivalent to area-weighted Lagrange-Galerkin schemes via a suitable definition of the basis functions, we will further prove that area-weighted Lagrange-Galerkin schemes represent a ``small" (more precisely, an $O(\Delta t$)) perturbation of exact Lagrange-Galerkin schemes. This equivalence implies a general result of stability for Semi-Lagrangian schemes.

Ferretti, R. (2013). On the relationship between Semi-Lagrangian and Lagrange-Galerkin schemes. NUMERISCHE MATHEMATIK, 124, 31-56 [10.1007/s00211-012-0505-5].

On the relationship between Semi-Lagrangian and Lagrange-Galerkin schemes

FERRETTI, Roberto
2013-01-01

Abstract

Following a previous result stating their equivalence under constant advection speed, Semi-Lagrangian and Lagrange-Galerkin schemes are compared in this paper in the situation of variable coefficient advection equations. Once known that Semi-Lagrangian schemes can be proved to be equivalent to area-weighted Lagrange-Galerkin schemes via a suitable definition of the basis functions, we will further prove that area-weighted Lagrange-Galerkin schemes represent a ``small" (more precisely, an $O(\Delta t$)) perturbation of exact Lagrange-Galerkin schemes. This equivalence implies a general result of stability for Semi-Lagrangian schemes.
2013
Ferretti, R. (2013). On the relationship between Semi-Lagrangian and Lagrange-Galerkin schemes. NUMERISCHE MATHEMATIK, 124, 31-56 [10.1007/s00211-012-0505-5].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/115592
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