$L^\infty$-Stability of IMEX-BDF2 Finite Volume Scheme for Convection-Diffusion Equation

Caterina Calgaro (1, 2) , Meriem Ezzoug (3)

1 RAPSODI - Reliable numerical approximations of dissipative systems
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 Département de Mathématiques [Monastir]

In this paper, we propose a finite volume scheme for solving a two-dimensional convection-diffusion equation on general meshes. This work is based on a implicit-explicit (IMEX) second order method and it is issued from the seminal paper [2]. In the framework of MUSCL methods, we will prove that the local maximum property is guaranteed under an explicit Courant-Friedrichs-Levy condition and the classical hypothesis for the triangulation of the domain.

Mots clés: IMEX-BDF2; L∞-stability; Convection-diffusion equation; finite volume scheme

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

Caterina Calgaro, Meriem Ezzoug. $L^\infty$-Stability of IMEX-BDF2 Finite Volume Scheme for Convection-Diffusion Equation. FVCA 2017: Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects, Jun 2017, Lille, France. pp.245-253, ⟨10.1007/978-3-319-57397-7_17⟩. ⟨hal-01574893⟩