Superconvergence and nonsuperconvergence of the shortley-weller approximations for dirichlet problems

Tetsuro Yamamoto; Qing Fang; Xiaojun Chen

doi:10.1081/NFA-100105113

Superconvergence and nonsuperconvergence of the shortley-weller approximations for dirichlet problems

Tetsuro Yamamoto
, Qing Fang
, Xiaojun Chen

Research output: Journal article publication › Journal article › Academic research › peer-review

16 Citations (Scopus)

Abstract

We are concerned with the numerical solutions of Dirichlet problems of elliptic equations. The convergence behavior of numerical solutions by using Shortley-Weller approximation is considered. We give three examples and prove that they have properties of nonsuperconvergence near any boundary point, superconvergence near a side and superconvergence near a corner, respectively.

Original language	English
Pages (from-to)	455-470
Number of pages	16
Journal	Numerical Functional Analysis and Optimization
Volume	22
Issue number	3-4
DOIs	https://doi.org/10.1081/NFA-100105113
Publication status	Published - 1 Jan 2001
Externally published	Yes

Keywords

Dirichlet problems
Finite difference methods
Shortley-Weller approximation
Superconvergence

ASJC Scopus subject areas

Analysis
Signal Processing
Computer Science Applications
Control and Optimization

More information

10.1081/NFA-100105113

Cite this

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abstract = "We are concerned with the numerical solutions of Dirichlet problems of elliptic equations. The convergence behavior of numerical solutions by using Shortley-Weller approximation is considered. We give three examples and prove that they have properties of nonsuperconvergence near any boundary point, superconvergence near a side and superconvergence near a corner, respectively.",

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AU - Yamamoto, Tetsuro

AU - Fang, Qing

AU - Chen, Xiaojun

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N2 - We are concerned with the numerical solutions of Dirichlet problems of elliptic equations. The convergence behavior of numerical solutions by using Shortley-Weller approximation is considered. We give three examples and prove that they have properties of nonsuperconvergence near any boundary point, superconvergence near a side and superconvergence near a corner, respectively.

AB - We are concerned with the numerical solutions of Dirichlet problems of elliptic equations. The convergence behavior of numerical solutions by using Shortley-Weller approximation is considered. We give three examples and prove that they have properties of nonsuperconvergence near any boundary point, superconvergence near a side and superconvergence near a corner, respectively.

KW - Dirichlet problems

KW - Finite difference methods

KW - Shortley-Weller approximation

KW - Superconvergence

UR - https://www.scopus.com/pages/publications/0035327016

U2 - 10.1081/NFA-100105113

DO - 10.1081/NFA-100105113

M3 - Journal article

SN - 0163-0563

VL - 22

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EP - 470

JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

IS - 3-4

ER -

Superconvergence and nonsuperconvergence of the shortley-weller approximations for dirichlet problems

Abstract

Keywords

ASJC Scopus subject areas

More information

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