On four numerical schemes for a unipolar degenerate drift-diffusion model

Clément Cancès (1, 2) , Claire Chainais-Hillairet (2, 1) , Jürgen Fuhrmann (3) , Benoît Gaudeul (2, 1)

1 RAPSODI - Reliable numerical approximations of dissipative systems
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 Numerical Mathematics and Scientific Computing [WIAS]

We consider a unipolar degenerate drift-diffusion system where the relation between the concentration of the charged species c and the chemical potential h is $h(c) = log(c/(1−c))$. For four different finite volume schemes based on four different formulations of the fluxes of the problem, we discuss stability and existence results. For two of them, we report a convergence proof. Numerical experiments illustrate the behaviour of the different schemes.

Mots clés: Finite Volume Methods; Drift-Diffusion Problems; Energy Methods

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

Clément Cancès, Claire Chainais-Hillairet, Jürgen Fuhrmann, Benoît Gaudeul. On four numerical schemes for a unipolar degenerate drift-diffusion model. Finite Volumes for Complex Applications IX, Jun 2020, Bergen, Norway. ⟨hal-02461524⟩