Solution of Fokker-Planck equation by finite element and finite difference methods for nonlinear systems

Numerical Solution of the Fokker-planck Equation by Finite Difference and Finite Element Methods - a Comparative Study

Finite element and finite difference methods have been widely used, among other methods, to numerically solve the Fokker-Planck equation for investigating the time history of the probability density function of linear and nonlinear 2d and 3d problems, and also the application to 4d problems has been addressed. However, due to the enormous increase of the computational costs, different strategie...

Application of multi-scale finite element methods to the solution of the Fokker–Planck equation

This paper presents an application of multi-scale finite element methods to the solution of the multi-dimensional Fokker–Planck equation. The Fokker–Planck, or forward Kolmogorov, equation is a degenerate convective–diffusion equation arising in Markov-Process theory. It governs the evolution of the transition probability density function of the response of a broad class of dynamical systems dr...

A Multiscale Finite Element Method for the Fokker Planck Equation

In a recent paper, the authors developed the framework for multi-scale finite element methods for the solution of the multi-dimensional Fokker-Planck equation in stochastic structural dynamics. The Fokker-Planck equation governs the evolution of the transition probability density function of the response of a broad class of dynamical systems driven by Gaussian noise, and completely describes th...

Finite Element Methods for Convection Diffusion Equation

This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...

Iterative methods for solving non linear Fokker-Planck equation