数学
耗散系统
离散化
应用数学
有限元法
平衡流
有限差分
能量(信号处理)
约束(计算机辅助设计)
福克-普朗克方程
空格(标点符号)
数学分析
有限差分法
订单(交换)
偏微分方程
几何学
计算机科学
物理
统计
财务
量子力学
经济
热力学
操作系统
作者
Jingwei Hu,Xiangxiong Zhang
出处
期刊:Ima Journal of Numerical Analysis
日期:2022-05-18
卷期号:43 (3): 1450-1484
被引量:4
标识
DOI:10.1093/imanum/drac014
摘要
Abstract In this work we introduce semi-implicit or implicit finite difference schemes for the continuity equation with a gradient flow structure. Examples of such equations include the linear Fokker–Planck equation and the Keller–Segel equations. The two proposed schemes are first-order accurate in time, explicitly solvable, and second-order and fourth-order accurate in space, which are obtained via finite difference implementation of the classical continuous finite element method. The fully discrete schemes are proved to be positivity preserving and energy dissipative: the second-order scheme can achieve so unconditionally while the fourth-order scheme only requires a mild time step and mesh size constraint. In particular, the fourth-order scheme is the first high order spatial discretization that can achieve both positivity and energy decay properties, which is suitable for long time simulation and to obtain accurate steady state solutions.
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