Flexible piecewise approximations based on partition of unity

Weimin Han; Wing Kam Liu

doi:10.1007/s10444-004-1810-z

Flexible piecewise approximations based on partition of unity

Weimin Han, Wing Kam Liu

Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

In this paper, we study a flexible piecewise approximation technique based on the use of the idea of the partition of unity. The approximations are piecewisely defined, globally smooth up to any order, enjoy polynomial reproducing conditions, and satisfy nodal interpolation conditions for function values and derivatives of any order. We present various properties of the approximations, that are desirable properties for optimal order convergence in solving boundary value problems.

Original language	English (US)
Pages (from-to)	191-199
Number of pages	9
Journal	Advances in Computational Mathematics
Volume	23
Issue number	1-2
DOIs	https://doi.org/10.1007/s10444-004-1810-z
State	Published - Jul 2005

Funding

∗Corresponding author. The work of this author was partially supported by NSF under grant DMS-0106781. ∗∗The work of this author was supported by NSF.

Keywords

Galerkin method
Nodal interpolation
Partition of unity
Polynomial reproducing
Smooth piecewise approximation

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1007/s10444-004-1810-z

Cite this

@article{b64467bdf9c343d995f14b5fb09a9831,

title = "Flexible piecewise approximations based on partition of unity",

abstract = "In this paper, we study a flexible piecewise approximation technique based on the use of the idea of the partition of unity. The approximations are piecewisely defined, globally smooth up to any order, enjoy polynomial reproducing conditions, and satisfy nodal interpolation conditions for function values and derivatives of any order. We present various properties of the approximations, that are desirable properties for optimal order convergence in solving boundary value problems.",

keywords = "Galerkin method, Nodal interpolation, Partition of unity, Polynomial reproducing, Smooth piecewise approximation",

author = "Weimin Han and Liu, {Wing Kam}",

note = "Funding Information: ∗Corresponding author. The work of this author was partially supported by NSF under grant DMS-0106781. ∗∗The work of this author was supported by NSF.",

year = "2005",

month = jul,

doi = "10.1007/s10444-004-1810-z",

language = "English (US)",

volume = "23",

pages = "191--199",

journal = "Advances in Computational Mathematics",

issn = "1019-7168",

publisher = "Springer Netherlands",

number = "1-2",

}

TY - JOUR

T1 - Flexible piecewise approximations based on partition of unity

AU - Han, Weimin

AU - Liu, Wing Kam

N1 - Funding Information: ∗Corresponding author. The work of this author was partially supported by NSF under grant DMS-0106781. ∗∗The work of this author was supported by NSF.

PY - 2005/7

Y1 - 2005/7

N2 - In this paper, we study a flexible piecewise approximation technique based on the use of the idea of the partition of unity. The approximations are piecewisely defined, globally smooth up to any order, enjoy polynomial reproducing conditions, and satisfy nodal interpolation conditions for function values and derivatives of any order. We present various properties of the approximations, that are desirable properties for optimal order convergence in solving boundary value problems.

AB - In this paper, we study a flexible piecewise approximation technique based on the use of the idea of the partition of unity. The approximations are piecewisely defined, globally smooth up to any order, enjoy polynomial reproducing conditions, and satisfy nodal interpolation conditions for function values and derivatives of any order. We present various properties of the approximations, that are desirable properties for optimal order convergence in solving boundary value problems.

KW - Galerkin method

KW - Nodal interpolation

KW - Partition of unity

KW - Polynomial reproducing

KW - Smooth piecewise approximation

UR - http://www.scopus.com/inward/record.url?scp=16244410108&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=16244410108&partnerID=8YFLogxK

U2 - 10.1007/s10444-004-1810-z

DO - 10.1007/s10444-004-1810-z

M3 - Article

AN - SCOPUS:16244410108

SN - 1019-7168

VL - 23

SP - 191

EP - 199

JO - Advances in Computational Mathematics

JF - Advances in Computational Mathematics

IS - 1-2

ER -

Flexible piecewise approximations based on partition of unity

Abstract

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this