$L^\infty$ bounds for numerical solutions of noncoercive convection-diffusion equations

Claire Chainais-Hillairet (1, 2) , Maxime Herda (2, 1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 RAPSODI - Reliable numerical approximations of dissipative systems

In this work, we apply an iterative energy method à la de Giorgi in order to establish $L^\infty$ bounds for numerical solutions of noncoercive convection-diffusion equations with mixed Dirichlet-Neumann boundary conditions.

Mots clés: finite volume schemes; uniform bounds; noncoercive elliptic equations

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

Claire Chainais-Hillairet, Maxime Herda. $L^\infty$ bounds for numerical solutions of noncoercive convection-diffusion equations. Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples., Jun 2020, Bergen, Norway. ⟨10.1007/978-3-030-43651-3_12⟩. ⟨hal-02404546v2⟩