Generalized Clenshaw-Curtis quadrature rule with application to a collocation least-squares method

Changho Kim; Sang Dong Kim; Jungho Yoon

doi:10.1016/j.amc.2007.01.095

Generalized Clenshaw-Curtis quadrature rule with application to a collocation least-squares method

Changho Kim, Sang Dong Kim, Jungho Yoon

Department of Mathematics

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

Abstract

This paper deals with an extension of one-dimensional Clenshaw-Curtis quadrature rule to R^d, d ≥ 2 on a convex domain. As one of its applications, we apply this quadrature rule to a collocation least-squares method using arbitrary abscissas for a first-order system of an elliptic boundary value problem so that the convergence analysis on a numerical solution can be shown in a standard Sobolev norm.

Original language	English
Pages (from-to)	781-789
Number of pages	9
Journal	Applied Mathematics and Computation
Volume	190
Issue number	1
DOIs	https://doi.org/10.1016/j.amc.2007.01.095
State	Published - 1 Jul 2007

Keywords

Clenshaw-Curtis quadrature rule
Collocation least-squares methods
First-order system

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10.1016/j.amc.2007.01.095

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title = "Generalized Clenshaw-Curtis quadrature rule with application to a collocation least-squares method",

abstract = "This paper deals with an extension of one-dimensional Clenshaw-Curtis quadrature rule to Rd, d ≥ 2 on a convex domain. As one of its applications, we apply this quadrature rule to a collocation least-squares method using arbitrary abscissas for a first-order system of an elliptic boundary value problem so that the convergence analysis on a numerical solution can be shown in a standard Sobolev norm.",

keywords = "Clenshaw-Curtis quadrature rule, Collocation least-squares methods, First-order system",

author = "Changho Kim and Kim, {Sang Dong} and Jungho Yoon",

note = "Funding Information: The second author is supported by the grant KRF-2005-070-C00017 and the third author is also supported by the grant R01-2006-000-10424-0 from Korea Science and Engineering Foundation in Ministry of Science & Technology. ",

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AU - Kim, Sang Dong

AU - Yoon, Jungho

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Y1 - 2007/7/1

N2 - This paper deals with an extension of one-dimensional Clenshaw-Curtis quadrature rule to Rd, d ≥ 2 on a convex domain. As one of its applications, we apply this quadrature rule to a collocation least-squares method using arbitrary abscissas for a first-order system of an elliptic boundary value problem so that the convergence analysis on a numerical solution can be shown in a standard Sobolev norm.

AB - This paper deals with an extension of one-dimensional Clenshaw-Curtis quadrature rule to Rd, d ≥ 2 on a convex domain. As one of its applications, we apply this quadrature rule to a collocation least-squares method using arbitrary abscissas for a first-order system of an elliptic boundary value problem so that the convergence analysis on a numerical solution can be shown in a standard Sobolev norm.

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KW - First-order system

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ER -

Generalized Clenshaw-Curtis quadrature rule with application to a collocation least-squares method

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Keywords

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