Superconvergence of solution derivatives of the Shortley-Weller difference approximation to Poisson's equation with singularities on polygonal domains

Z-C. Li; H-Y. Hu; Song Wang; Q. Fang

doi:10.1016/j.apnum.2007.02.007

Superconvergence of solution derivatives of the Shortley-Weller difference approximation to Poisson's equation with singularities on polygonal domains

Z-C. Li, H-Y. Hu, Song Wang, Q. Fang

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

13 Citations (Scopus)

Abstract

This paper presents a superconvergence analysis for the Shortley-Weller finite difference approximation of Poisson's equation with unbounded derivatives on a polygonal domain. In this analysis, we first formulate the method as a special finite element/volume method. We then analyze the convergence of the method in a finite element framework. An O(h(1.5))-order superconvergence is derived for the solution derivatives in a discrete H 1 norm. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	689-704
Journal	Applied Numerical Mathematics
Volume	58
DOIs	https://doi.org/10.1016/j.apnum.2007.02.007
Publication status	Published - 2008

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title = "Superconvergence of solution derivatives of the Shortley-Weller difference approximation to Poisson's equation with singularities on polygonal domains",

abstract = "This paper presents a superconvergence analysis for the Shortley-Weller finite difference approximation of Poisson's equation with unbounded derivatives on a polygonal domain. In this analysis, we first formulate the method as a special finite element/volume method. We then analyze the convergence of the method in a finite element framework. An O(h(1.5))-order superconvergence is derived for the solution derivatives in a discrete H 1 norm. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved.",

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AU - Li, Z-C.

AU - Hu, H-Y.

AU - Wang, Song

AU - Fang, Q.

PY - 2008

Y1 - 2008

N2 - This paper presents a superconvergence analysis for the Shortley-Weller finite difference approximation of Poisson's equation with unbounded derivatives on a polygonal domain. In this analysis, we first formulate the method as a special finite element/volume method. We then analyze the convergence of the method in a finite element framework. An O(h(1.5))-order superconvergence is derived for the solution derivatives in a discrete H 1 norm. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved.

AB - This paper presents a superconvergence analysis for the Shortley-Weller finite difference approximation of Poisson's equation with unbounded derivatives on a polygonal domain. In this analysis, we first formulate the method as a special finite element/volume method. We then analyze the convergence of the method in a finite element framework. An O(h(1.5))-order superconvergence is derived for the solution derivatives in a discrete H 1 norm. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved.

U2 - 10.1016/j.apnum.2007.02.007

DO - 10.1016/j.apnum.2007.02.007

M3 - Article

VL - 58

SP - 689

EP - 704

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

ER -

Superconvergence of solution derivatives of the Shortley-Weller difference approximation to Poisson's equation with singularities on polygonal domains

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