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arXiv · 1710.03471

Convergence analysis of a finite element approximation of minimum action methods

Xiaoliang Wan·Haijun Yu·Jiayu Zhai
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Abstract

In this work, we address the convergence of a finite element approximation of the minimizer of the Freidlin-Wentzell (F-W) action functional for non-gradient dynamical systems 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 elements, and establish the convergence of {the approximation} through $\Gamma$-convergence.

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Xiaoliang Wan, Haijun Yu, Jiayu Zhai. 2017-10-10. Convergence analysis of a finite element approximation of minimum action methods. https://doi.org/10.1137/17m1141679

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