We are interested in the discretisation of a drift-diffusion system in the framework of hybrid finite volume (HFV) methods on general polygonal/polyhedral meshes. The system under study is composed of two anisotropic and nonlinear convection-diffusion equations coupled with a Poisson equation and describes in particular semi-conductor devices immersed in a magnetic field. We introduce a new scheme based on an entropy-dissipation relation and prove that the scheme admits solutions with values in admissible sets - especially, the computed densities remain positive. Moreover, we show that the discrete solutions to the scheme converge exponentially fast in time towards the associated discrete thermal equilibrium. Several numerical tests confirm our theoretical results.

翻译：我们感兴趣的是,在普通多边形/多光速介质的混合有限体积方法的框架内,将漂流扩散系统分解为一种离散系统,正在研究的系统由两种厌异性和非线性对流扩散方程式组成,同时配以Poisson方程式,并特别描述浸入磁场的半导体装置。我们引入了一种基于诱导分解关系的新办法,并证明该办法接受以可接受组数计值的解决方案,特别是计算密度仍为正数。此外,我们表明,该办法的离散解决办法在时间上迅速接近相关的离散热平衡。一些数字测试证实了我们的理论结果。