Analysis of moving least squares approximation revisited

TL;DR

This paper revisits the error estimation of moving least squares approximation for functions in fractional Sobolev spaces, extending previous results and clarifying mathematical details, with applications to Galerkin methods for PDEs.

Contribution

It extends existing error estimates for moving least squares approximation to fractional Sobolev spaces and provides detailed mathematical analysis and applications to PDE solving.

Findings

Extended error bounds for fractional Sobolev spaces

Clarified mathematical details in error estimation

Applied analysis to Galerkin methods for PDEs

Abstract

In this article the error estimation of the moving least squares approximation is provided for functions in fractional order Sobolev spaces. The analysis presented in this paper extends the previous estimations and explains some unnoticed mathematical details. An application to Galerkin method for partial differential equations is also supplied.