In this article, we are interested in the asymptotic analysis of a finite volume scheme for one dimensional linear kinetic equations, with either Fokker-Planck or linearized BGK collision operator. Thanks to appropriate uniform estimates, we establish that the proposed scheme is Asymptotic-Preserving in the diffusive limit. Moreover, we adapt to the discrete framework the hypocoercivity method proposed by [J. Dolbeault, C. Mouhot and C. Schmeiser, Trans. Amer. Math. Soc., 367, 6 (2015)] to prove the exponential return to equilibrium of the approximate solution. We obtain decay rates that are bounded uniformly in the diffusive limit.
Finally, we present an efficient implementation of the proposed numerical schemes, and perform numerous numerical simulations assessing their accuracy and efficiency in capturing the correct asymptotic behaviors of the models.
Hypocoercivity based Sensitivity Analysis and Spectral Convergence of the Stochastic Galerkin Approximation to Collisional Kinetic Equations with Multiple Scales and Random Inputs
The Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin（德克萨斯大学奥斯汀分校计算工程与科学研究所）；Department of Mathematics, University of Wisconsin-Madison（威斯康星大学麦迪逊分校数学系）
Discrete $H$-theorem for a finite volume discretization of a nonlinear kinetic system: application to hypocoercivity
Nantes Université, CNRS, Laboratoire de Mathématiques Jean Leray, LMJL（南特大学，法国国家科学研究中心，让·勒雷数学实验室）；Univ Brest, CNRS UMR 6205, Laboratoire de Mathématiques de Bretagne Atlantique（布雷斯特大学，法国国家科学研究中心，布列塔尼大西洋数学实验室）；Université Côte d’Azur, CNRS, LJAD（蔚蓝海岸大学，法国国家科学研究中心，拉雅德数学实验室）
Hypocoercivity-preserving space-time Galerkin methods for kinetic Fokker-Planck equations
Inria（法国国家信息与自动化研究所）；CERMICS, ENPC, Institut Polytechnique de Paris, CNRS（巴黎高等师范学院计算数学与计算机科学中心，巴黎理工学院，法国国家科学研究中心）；The Maxwell Institute for Mathematical Sciences and Department of Mathematics, Heriot-Watt University（赫瑞-瓦特大学麦克斯韦数学科学研究所及数学系）；Department of Mathematics, School of Applied Mathematical and Physical Sciences, National Technical University of Athens（雅典国立技术大学应用数学与物理科学学院数学系）；Institute of Applied and Computational Mathematics, FORTH（希腊基础与研究基金会应用与计算数学研究所）
A hypocoercivity-exploiting stabilised finite element method for Kolmogorov equation
Inria（法国国家信息与自动化研究所）；Ecole des Ponts（巴黎路桥学校）；Maxwell Institute for Mathematical Sciences and Department of Mathematics, School of Mathematical and Computer Sciences, Heriot-Watt University（赫瑞-瓦特大学数学与计算机科学学院数学系麦克斯韦数学科学研究所）；Department of Mathematics, School of Applied Mathematical and Physical Sciences, National Technical University of Athens（雅典国立技术大学应用数理科学学院数学系）；IACM-FORTH（希腊科学院计算数学研究所）；Department of Mathematics, University of Sussex（萨塞克斯大学数学系）
Asymptotic numerical hypocoercivity of the space-time discontinuous Galerkin method for the Kolmogorov equation
Inria（法国国家信息与自动化研究所）；CERMICS, ENPC, Institut Polytechnique de Paris, CNRS（巴黎高等师范学院计算数学与控制系统中心，巴黎理工学院，法国国家科学研究中心）；The Maxwell Institute for Mathematical Sciences & Department of Mathematics, Heriot-Watt University（爱丁堡赫瑞瓦特大学麦克斯韦数学科学研究所及数学系）；Department of Mathematics, School of Applied Mathematical and Physical Sciences, National Technical University of Athens（雅典国立技术大学应用数学与物理科学学院数学系）；IACM-FORTH（希腊科学与数学研究所计算数学中心）；Department of Mathematics, University of Sussex（英国萨塞克斯大学数学系）
Provably realizability-preserving finite volume method for quadrature-based moment models of kinetic equations
Southern University of Science and Technology（南方科技大学）；Institute of Applied Analysis and Numerical Simulation, University of Stuttgart（斯图加特大学应用分析与数值模拟研究所）
Convergence of the Finite Volume Method for scalar conservation laws with multiplicative noise: an approach by kinetic formulation
Aix-Marseille Université, CNRS, Centrale Marseille, I2M（艾克斯-马赛大学）；Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan（里昂大学，克莱贝尔·里昂第一大学）
