CONVERGENCE ANALYSIS OF A FINITE ELEMENT APPROXIMATION OF MINIMUM ACTION METHODS

In this work, we address the convergence of a finite element approximation of the minimizer of the Preidlin-Wentzell (F-W) action functional for nongradient 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 Γ-convergence.