Convergence analysis of reproducing kernel particle method to elliptic eigenvalue problem

In this work we aim to provide a fundamental theory of the reproducing kernel particle method for solving elliptic eigenvalue problems. We concentrate on the convergence analysis of eigenvalues and eigenfunctions, as well as the optimal estimations which are shown to be related to the reproducing degree, support size, and overlapping number in the reproducing kernel approximation. The theoretical analysis has also demonstrated that the order of convergence for eigenvalues is in the square of the order of convergence for eigenfunctions. Numerical results are also presented to validate the theoretical analysis.