Exponential decay to equilibrium of nonlinear DDFV schemes for convection-diffusion equations

Claire Chainais-Hillairet (1) , Stella Krell (2, 3, 4, 5)

1 RAPSODI - Reliable numerical approximations of dissipative systems
2 COFFEE - COmplex Flows For Energy and Environment
3 COMUE UCA - COMUE Université Côte d'Azur (2015-2019)
4 LJAD - Laboratoire Jean Alexandre Dieudonné
5 UniCA - Université Côte d'Azur

We introduce a nonlinear DDFV scheme for an anisotropic linear convection-diffusion equationwith mixed boundary conditions and we establish the exponential decay of the scheme towards its steady-state.

Mots clés: Discrete Duality Finite Volume scheme; discrete entropy/dissipation relation; long time behaviour

Domaines: Analyse numérique [math.NA]

Claire Chainais-Hillairet, Stella Krell. Exponential decay to equilibrium of nonlinear DDFV schemes for convection-diffusion equations. FVCA 2020 - 9th Conference on Finite Volumes for Complex Applications, Jun 2020, Bergen, Norway. ⟨hal-02408212⟩