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In a foregoing paper [Sonar, ESAIM: M2AN 39 (2005) 883-908] we analyzed the Interpolating Moving Least Squares (IMLS) method due to Lancaster and Šalkauskas with respect to its approximation powers and derived finite difference expressions for the derivatives. In this sequel we follow a completely different approach to the IMLS method given by Kunle [Dissertation (2001)]. As a typical problem with IMLS method we address the question of getting admissible results at the boundary by introducing “ghost points”. Most interesting in IMLS methods are the finite difference operators which can be computed from different choices of basis functions and weight functions. We present a way of deriving these discrete operators in the spatially one-dimensional case. Multidimensional operators can be constructed by simply extending our approach to higher dimensions. Numerical results ranging from 1-d interpolation to the solution of PDEs are given.
@article{M2AN_2007__41_5_959_0,
author = {Netuzhylov, Hennadiy and Sonar, Thomas and Yomsatieankul, Warisa},
title = {Finite difference operators from moving least squares interpolation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {959--974},
publisher = {EDP-Sciences},
volume = {41},
number = {5},
year = {2007},
doi = {10.1051/m2an:2007042},
mrnumber = {2363891},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007042/}
}
TY - JOUR AU - Netuzhylov, Hennadiy AU - Sonar, Thomas AU - Yomsatieankul, Warisa TI - Finite difference operators from moving least squares interpolation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2007 SP - 959 EP - 974 VL - 41 IS - 5 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007042/ DO - 10.1051/m2an:2007042 LA - en ID - M2AN_2007__41_5_959_0 ER -
%0 Journal Article %A Netuzhylov, Hennadiy %A Sonar, Thomas %A Yomsatieankul, Warisa %T Finite difference operators from moving least squares interpolation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2007 %P 959-974 %V 41 %N 5 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007042/ %R 10.1051/m2an:2007042 %G en %F M2AN_2007__41_5_959_0
Netuzhylov, Hennadiy; Sonar, Thomas; Yomsatieankul, Warisa. Finite difference operators from moving least squares interpolation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 41 (2007) no. 5, pp. 959-974. doi: 10.1051/m2an:2007042
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