Meshless Galerkin algorithms for boundary integral equations with moving least square approximations

Authors:
Xiaolin Li
Affiliations:
College of Mathematics Science, Chongqing Normal University, Chongqing 400047, PR China
Venue:
Applied Numerical Mathematics
Year:
2011

Citing 9
Cited 2

The approximation power of moving least-squares

Mathematics of Computation
Error estimates for moving least square approximations

Applied Numerical Mathematics
Error Estimates in Sobolev Spaces for Moving Least Square Approximations

SIAM Journal on Numerical Analysis
Good quality point sets and error estimates for moving least square approximations

Applied Numerical Mathematics - Special issue on applied and computational mathematics: Selected papers of the fourth PanAmerican workshop
Error estimates for the finite point method

Applied Numerical Mathematics
Meshless Local Petrov--Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity

Applied Numerical Mathematics
On a two-level element-free Galerkin method for incompressible fluid flow

Applied Numerical Mathematics
A Galerkin boundary node method and its convergence analysis

Journal of Computational and Applied Mathematics
A meshless based method for solution of integral equations

Applied Numerical Mathematics

On error estimator and adaptivity in the meshless Galerkin boundary node method

Computational Mechanics
The Galerkin boundary node method for magneto-hydrodynamic (MHD) equation

Journal of Computational Physics

Quantified Score

Hi-index	0.01

Visualization

Abstract

In this paper, we first give error estimates for the moving least square (MLS) approximation in the H^k norm in two dimensions when nodes and weight functions satisfy certain conditions. This two-dimensional error results can be applied to the surface of a three-dimensional domain. Then combining boundary integral equations (BIEs) and the MLS approximation, a meshless Galerkin algorithm, the Galerkin boundary node method (GBNM), is presented. The optimal asymptotic error estimates of the GBNM for three-dimensional BIEs are derived. Finally, taking the Dirichlet problem of Laplace equation as an example, we set up a framework for error estimates of the GBNM for boundary value problems in three dimensions.