Numerical analysis of DDFV schemes for semiconductors energy-transport models

This article addresses the construction and the numerical analysis of implicit Discrete Duality Finite Volume schemes for a semiconductors' energy-transport model. The considered energy-transport model is presented in its scaled version as well as in a symmetrized form which involves entropy variables. We propose implicit in time numerical schemes for both the original system and its symmetrized form. As in the continuous framework, the numerical analysis is based on the reformulation of the PDE system using the set of entropic variables. The equivalence of both schemes allows to establish a discrete entropy inequality and consequently an priori estimates. As a by-product, existence of solutions to the schemes is proved by means of a Leray-Schauder argument. Numerical evidences allow to compare the performances of both schemes on the test case of a 2D ballistic diode.