Finite element approximation for the fractional eigenvalue problem

TL;DR

This paper develops a finite element method to approximate eigenvalues of the fractional Laplacian, proving convergence and convergence rate, supported by numerical experiments comparing with existing methods.

Contribution

It introduces a finite element approach for the fractional Laplacian eigenvalue problem with proven convergence and order, advancing numerical analysis in this area.

Findings

Discrete eigenvalues converge to continuous ones

Established the order of convergence

Numerical results align with theoretical predictions

Abstract

The purpose of this work is to study a finite element method for finding solutions to the eigenvalue problem for the fractional Laplacian. We prove that the discrete eigenvalue problem converges to the continuous one and we show the order of such convergence. Finally, we perform some numerical experiments and compare our results with previous work by other authors.