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

Abstract

In this paper, we propose a finite volume scheme for solving a twodimensional 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.