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Convergence analysis of reproducing kernel particle method to elliptic eigenvalue problem
Author(s) -
Hu HsinYun,
Chen JiunShyan
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22757
Subject(s) - mathematics , eigenvalues and eigenvectors , eigenfunction , convergence (economics) , kernel (algebra) , mathematical analysis , pure mathematics , physics , quantum mechanics , economics , economic growth
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.