Lie group stability of finite difference schemes

Emma Hoarau (1) , Claire David (2) , Pierre Sagaut (2) , Thiên-Hiêp Lê (1)

1 ONERA - The French Aerospace Lab [Châtillon]
2 LMM - Laboratoire de modélisation en mécanique

Differential equations arising in fluid mechanics are usually derived from the intrinsic properties of mechanical systems, in the form of conservation laws, and bear symmetries, which are not generally preserved by a finite difference approximation, and leading to inaccurate numerical results. This paper proposes a method that enables us to build a scheme that preserves some of those symmetries.

Mots clés: Lie group; differential approximation; invariant scheme

Domaines: Analyse numérique [math.NA]

Emma Hoarau, Claire David, Pierre Sagaut, Thiên-Hiêp Lê. Lie group stability of finite difference schemes. Supplement edition of the journal Discrete and Continuous Dynamical Systems, 2007, France. ⟨hal-00090421v2⟩