Premium
A study on the convergence of least‐squares meshfree method under inaccurate integration
Author(s) -
Park SangHoon,
Kwon KieChan,
Youn SungKie
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.613
Subject(s) - convergence (economics) , numerical integration , galerkin method , mathematics , meshfree methods , least squares function approximation , bounded function , moving least squares , finite element method , error analysis , mathematical optimization , work (physics) , computer science , mathematical analysis , structural engineering , engineering , mechanical engineering , statistics , estimator , economics , economic growth
In the authors' previous work, it has been shown through numerical examples that the least‐squares meshfree method (LSMFM) is highly robust to the integration errors while the Galerkin meshfree method is very sensitive to them. A mathematical study on the convergence of the solution of LSMFM under inaccurate integration is presented. New measures are introduced to take into account the integration errors in the error estimates. It is shown that, in LSMFM, solution errors are bounded by approximation errors even when integration is not accurate. Copyright © 2003 John Wiley & Sons, Ltd.