Coercivity, hypocoercivity, exponential time decay and simulations for\n discrete Fokker-Planck equations

2018/02/06 by Guillaume Dujardin, Frédéric Hérau, Dujardin, Guillaume +3 · 2 citations
Decision Sciences · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.1802.02173

openalex publication_date 2018/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this article, we propose and study several discrete versions of\nhomogeneous and inhomogeneous one-dimensional Fokker-Planck equations. In\nparticular, for these discretizations of velocity and space, we prove the\nexponential convergence to the equilibrium of the solutions, for\ntime-continuous equations as well as for time-discrete equations. Our method\nuses new types of discrete Poincar 'e inequalities for a "two-direction"\ndiscretization of the derivative in velocity. For the inhomogeneous problem, we\nadapt hypocoercive methods to the discrete cases.\n

Cited by

• Discrete H-theorem for a finite volume discretization of a nonlinear kinetic system: application to hypocoercivity
• On the discrete Poincaré inequality for B-schemes of 1D Fokker-Planck equations in full space

Related

• On the discrete Poincaré inequality for B-schemes of 1D Fokker-Planck equations in full space
• Long-time behavior for discretization schemes of Fokker-Planck equations via couplings
• Discretizing the Fokker-Planck equation with second-order accuracy: a dissipation driven approach
• Optimal non-symmetric Fokker-Planck equation for the convergence to a given equilibrium
• On a structure-preserving numerical method for fractional Fokker-Planck\n equations