On high-accuracy L∞-stable IMEX schemes for scalar hyperbolic multi-scale equations

Victor Michel-Dansac (1, 2) , Andrea Thomann (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 INSA Toulouse - Institut National des Sciences Appliquées - Toulouse
3 Dipartimento di Scienze e Alta Tecnologia

We present a framework to build high-accuracy IMEX schemes that fulfill the maximum principle, applied to a scalar hyperbolic multi-scale equation. Motivated by the findings in [Gottlieb, Shu, Tadmor, 2001] that implicit R-K schemes are not L∞-stable, our scheme, for which we can prove the L ∞ stability, is based on a convex combination between a first-order and a class of second-order IMEX schemes. We numerically demonstrate the advantages of our scheme, especially for discontinuous problems, and give a MOOD procedure to increase the accuracy.

Mots clés: L∞ stability; IMEX R-K schemes; MOOD; hyperbolic multi-scale equations

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Victor Michel-Dansac, Andrea Thomann. On high-accuracy L∞-stable IMEX schemes for scalar hyperbolic multi-scale equations. 2019. ⟨hal-02303491v1⟩