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 behavior of the whole numerical scheme.

中文翻译：

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半导体能量传输模型的数值方案分析

介绍了单极能量传输模型的一些有限体积方案。使用对偶熵变量的重新表述，我们可以通过控制离散熵耗散来显示离散熵的衰减。我们建立了一个先验估计，导致该方案的解决方案的存在。与连续框架类似，我们证明了离散相对熵对热平衡的指数衰减。数值结果评估了整个数值方案的良好行为。