Analysis of numerical schemes for semiconductors energy-transport models

Marianne Bessemoulin-Chatard (1) , Claire Chainais-Hillairet (2) , Hélène Mathis (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 RAPSODI - Reliable numerical approximations of dissipative systems

Some finite volume schemes for unipolar energy-transport models are introduced. Using a reformulation in dual entropy variables, we can show the decay of a discrete entropy with control of the discrete entropy dissipation. We establish a priori estimates which lead to the existence of a solution to the scheme. Similarly to the continuous framework, we prove the exponential decay of the discrete relative entropy towards the thermal equilibrium. Numerical results assess the good behaviour of the whole numerical scheme.

Mots clés: Energy-transport model; Finite volume schemes; Entropy method

Domaines: Analyse numérique [math.NA]

Marianne Bessemoulin-Chatard, Claire Chainais-Hillairet, Hélène Mathis. Analysis of numerical schemes for semiconductors energy-transport models. Applied Numerical Mathematics, 2021, 168, pp.143-169. ⟨10.1016/j.apnum.2021.05.030⟩. ⟨hal-02940224v2⟩