Finite volume $L^\infty$-stability for hyperbolic scalar problems

Stéphane Clain (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

A new formalism and tools are proposed to characterize high-order reconstructions in the finite volume method context. We introduce the notion of admissible reconstruction and investigate the maximum principle and positivity preserving properties for scalar hyperbolic problem using the new formalism. We show that the traditional limiting strategies cast in out formalism and provide new proves of the $L^\infty$ stability.

Mots clés: finite volume scheme; $L^\infty$ stability; maximum principle; high-order reconstruction; positivity preserving

Domaines: Analyse numérique [math.NA]

Stéphane Clain. Finite volume $L^\infty$-stability for hyperbolic scalar problems. 2010. ⟨hal-00467650⟩