A study on the convergence of least-squares meshfree method under inaccurate integration

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