# Difference operators from interpolating moving least squares and their deviation from optimality

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 39, Issue: 5, page 883-908
- ISSN: 0764-583X

## Access Full Article

top## Abstract

top## How to cite

topSonar, Thomas. "Difference operators from interpolating moving least squares and their deviation from optimality." ESAIM: Mathematical Modelling and Numerical Analysis 39.5 (2010): 883-908. <http://eudml.org/doc/194292>.

@article{Sonar2010,

abstract = {
We consider the classical Interpolating Moving Least Squares (IMLS)
interpolant as defined by Lancaster and Šalkauskas [Math. Comp.37 (1981)
141–158] and
compute the first and second derivative of this interpolant at the nodes of a
given grid with the help of a basic lemma on Shepard interpolants. We compare
the difference formulae with those defining optimal finite difference methods and
discuss their deviation from optimality.
},

author = {Sonar, Thomas},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Difference operators; moving least squares interpolation; order of approximation.; order of approximation; Shepard interpolant},

language = {eng},

month = {3},

number = {5},

pages = {883-908},

publisher = {EDP Sciences},

title = {Difference operators from interpolating moving least squares and their deviation from optimality},

url = {http://eudml.org/doc/194292},

volume = {39},

year = {2010},

}

TY - JOUR

AU - Sonar, Thomas

TI - Difference operators from interpolating moving least squares and their deviation from optimality

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 39

IS - 5

SP - 883

EP - 908

AB -
We consider the classical Interpolating Moving Least Squares (IMLS)
interpolant as defined by Lancaster and Šalkauskas [Math. Comp.37 (1981)
141–158] and
compute the first and second derivative of this interpolant at the nodes of a
given grid with the help of a basic lemma on Shepard interpolants. We compare
the difference formulae with those defining optimal finite difference methods and
discuss their deviation from optimality.

LA - eng

KW - Difference operators; moving least squares interpolation; order of approximation.; order of approximation; Shepard interpolant

UR - http://eudml.org/doc/194292

ER -

## References

top- T. Belytschko, Y. Krongauz, D. Organ, M. Fleming and P. Krysl, Meshless methods: an overview and recent developments. Comput. Methods Appl. Mech. Engrg.139 (1996) 3–47. Zbl0891.73075
- J.P. Boyd, Chebyshev and Fourier Spectral Methods. Springer Verlag (1989). Zbl0681.65079
- B. Fornberg, Generation of Finite Difference Formulas on Arbitrarily Spaced Grids. Math. Comp.51 (1988) 699–706. Zbl0701.65014
- B. Fornberg, A Practical Guide to Pseudospectral Methods. Cambridge University Press (1996). Zbl0844.65084
- J. Fürst and Th. Sonar, On meshless collocation approximations of conservation laws: preliminary investigations on positive schemes and dissipation models. ZAMM Z. Angew. Math. Mech.81 (2001) 403–415. Zbl0985.65123
- M. Kunle, Entwicklung und Untersuchung von Moving Least Square Verfahren zur numerischen Simulation hydrodynamischer Gleichungen. Doktorarbeit, Fakultät für Physik, Eberhard-Karls-Universität zu Tübingen (2001).
- P. Lancaster and K. Šalkauskas, Surfaces generated by moving least squares methods. Math. Comp.37 (1981) 141–158. Zbl0469.41005
- P. Lancaster and K. Šalkauskas, Curve and Surface Fitting: An Introduction. Academic Press (1986). Zbl0649.65012
- T. Liszka and J. Orkisz, The finite difference method at arbitrary irregular grids and its application in applied mechanics. Comput. Structures11 (1980) 83–95. Zbl0427.73077
- H. Netuzylov, Th. Sonar and W. Yomsatieankul, Finite difference operators from moving least squares interpolation. Manuscript, Institut Computational Mathematics, TU Braunschweig (2004).
- N. Perrone and R. Kao, A general finite difference method for arbitrary meshes. Comput. Structures5 (1975) 45–58.
- W. Schönauer, Generation of difference and error formulae of arbitrary consistency order on an unstructured grid. ZAMM Z. Angew. Math. Mech.78 (1998) S1061–S1062. Zbl0925.65175
- L. Theilemann, Ein gitterfreies differenzenverfahren. Doktorarbeit, Institut für Aerodynamik und Gasdynamik, Universität Stuttgart (1983).
- W. Yomsatieankul, Th. Sonar and H. Netuzhylov, Spatial difference operators from moving least squares interpolation. Manuscript, Institut Computational Mathematics, TU Braunschweig (2004).

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.