Study of a fully implicit scheme for the drift-diffusion system. Asymptotic behavior in the quasi-neutral limit
Université de Nantes（南特大学）；Laboratoire de Mathématiques Jean Leray, UMR 6629 - CNRS（让·勒雷数学实验室，UMR 6629 - 法国国家科学研究中心）；Université Lille 1（里尔第一大学）；Laboratoire P. Painlevé, CNRS UMR 8524（P. 庞加莱数学实验室，CNRS UMR 8524）；INRIA Lille Nord Europe（欧洲北部法国国家信息与自动化研究所）；Institut de Mathématiques de Toulouse, CNRS UMR 5219（图卢兹数学研究所，CNRS UMR 5219）；Université de Toulouse（图卢兹大学）
In this paper, we are interested in the numerical approximation of the classical time-dependent drift-diffusion system near quasi-neutrality. We consider a fully implicit in time and finite volume in space scheme, where the convection-diffusion fluxes are approximated by Scharfetter-Gummel fluxes. We establish that all the a priori estimates needed to prove the convergence of the scheme does not depend on the Debye length $λ$. This proves that the scheme is asymptotic preserving in the quasi-neutral limit $λ\to 0$.
Relative entropy estimate and geometric ergodicity for implicit Langevin Monte Carlo
School of Mathematical Sciences, Institute of Natural Sciences, MOE-LSC, Shanghai Jiao Tong University（上海交通大学数学科学学院、自然科学研究院、教育部线性科学中心）；Department of Mathematics, Duke University（杜克大学数学系）；Department of Physics, Duke University（杜克大学物理系）
本文研究隐式 Langevin Monte Carlo 方法，在漂移仅单边 Lipschitz 条件下，利用 PDE 技术和反射型耦合方法证明了相对熵误差界与 Wasserstein-1 距离下的几何遍历性，并将误差界推广到时间一致情形。
Strong Convergence of the Linear Implicit Euler Method for the Finite Element Discretization of Semilinear SPDEs Driven by Multiplicative and Additive Noise
Convergence rate and exponential stability of backward Euler method for neutral stochastic delay differential equations under generalized monotonicity conditions
Mean-square stability and error analysis of implicit time-stepping schemes for linear parabolic SPDEs with multiplicative Wiener noise in the first derivative
Exponential decay of a finite volume scheme to the thermal equilibrium for drift--diffusion systems
Univ. Nantes, CNRS, UMR 6629 - Laboratoire Jean Leray（南特大学，法国国家科学研究中心，联合研究单位6629-让·勒雷实验室）；Univ. Lille, CNRS, UMR 8524 - Laboratoire Paul Painlevé（里尔大学，法国国家科学研究中心，联合研究单位8524-保罗·潘勒韦实验室）
Pathwise convergence of a novel numerical scheme based on semi-implicit method for stochastic differential-algebraic equations with non-global Lipschitz coefficients
