Stochastic Convergence of A Nonconforming Finite Element Method for the Thin Plate Spline Smoother for Observational Data

摘要

The thin plate spline smoother is a classical model for fnding a smoothfunction from the knowledge of its observation at scattered locations which mayhave random noises. We consider a nonconforming Morley finite element method toapproximate the model. We prove the stochastic convergence of the finiteelement method which characterizes the tail property of the probabilitydistribution function of the finite element error. We also propose aself-consistent iterative algorithm to determine the smoothing parameter basedon our theoretical analysis. Numerical examples are included to confirm thetheoretical analysis and to show the competitive performance of the self-consistent algorithm for finding the smoothing parameter.