论文标题
结构保留不可逆过程的Fokker-Planck方程的方案
Structure preserving schemes for Fokker-Planck equations of irreversible processes
论文作者
论文摘要
在本文中，我们通过有限元元素方法的有限差差实现来介绍二阶和第四阶空间离散化，以求解与不可逆过程相关的Fokker-Planck方程。所提出的方案是时间和二阶和太空中的第四阶。在平滑溶液的轻度网格条件和时间步长的限制下，这些方案被证明是单调的，因此具有阳性性和能量耗散性。特别是，我们的方案适合在大的最后时间模拟中捕获稳态解决方案。
In this paper, we introduce second order and fourth order space discretization via finite difference implementation of the finite element method for solving Fokker-Planck equations associated with irreversible processes. The proposed schemes are first order in time and second order and fourth order in space. Under mild mesh conditions and time step constraints for smooth solutions, the schemes are proved to be monotone, thus are positivity-preserving and energy dissipative. In particular, our scheme is suitable for capturing steady state solutions in large final time simulations.
