Convergence analysis of finite element approximation of large deviation principle

Xiaoliang Wan, Haijun Yu, Jiayu Zhai

Published 2017-10-10Version 1

In this work, we address the convergence of the finite element approximation of the minimizer of the Freidlin-Wentzell (F-W) action functional for a non-gradient dynamical system perturbed by small noise. The F-W theory of large deviations is a rigorous mathematical tool to study small-noise-induced transitions in a dynamical system. The central task in the application of F-W theory of large deviations is to seek the minimizer and minimum of the F-W action functional. We discretize the F-W action functional using linear finite element, and establish the convergence of the approximate minimizer through $\Gamma$-convergence.