We are interested in the long-time behaviour of approximate solutions to heterogeneous and anisotropic linear advection-diffusion equations in the framework of hybrid finite volume (HFV) methods on general polygonal/polyhedral meshes. We consider two linear methods, as well as a new, nonlinear scheme, for which we prove the existence and the positivity of discrete solutions. We show that the discrete solutions to the three schemes converge exponentially fast in time towards the associated discrete steady-states. To illustrate our theoretical findings, we present some numerical simulations assessing long-time behaviour and positivity. We also compare the accuracy of the schemes on some numerical tests in the stationary case.

翻译：我们感兴趣的是,在一般多边形/波利希德模类混合有限体积(HFV)方法的框架内,对异异性和异性直线对流扩散方程式的近似解决办法的长期行为,我们考虑了两种线性方法,以及一种新的非线性办法,为此,我们证明了离散解决办法的存在和现实性。我们表明,三种办法的离散解决办法在相关离散稳定状态的时间内迅速迅速向相关离散稳定状态汇合。为了说明我们的理论结论,我们提出了一些数字模拟,评估长期行为和可视性。我们还比较了固定情况下某些数字试验办法的准确性。