Improved difference schemes for the Dirichlet problem of Poisson's equation in the neighbourhood of corners

C. Zenger; H. Gietl

doi:10.1007/BF01411846

Improved difference schemes for the Dirichlet problem of Poisson's equation in the neighbourhood of corners

C. Zenger
, H. Gietl

Leibniz Rechenzentrum München

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

20 Scopus citations

Abstract

The standard 5-point difference scheme for the model problem Δu=f on a special polygonal domain with given boundary values is modified at a few points in the neighbourhood of the corners in such a way that the order of convergence at interior points is the same as in the case of a smooth boundary. As a side result improved error bounds for the usual method in the neighbourhood of corners are given.

Original language	English
Pages (from-to)	315-332
Number of pages	18
Journal	Numerische Mathematik
Volume	30
Issue number	3
DOIs	https://doi.org/10.1007/BF01411846
State	Published - Sep 1978
Externally published	Yes

Keywords

Subject Classifications: AMS(MOS):65N10, CR:5.17

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10.1007/BF01411846

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title = "Improved difference schemes for the Dirichlet problem of Poisson's equation in the neighbourhood of corners",

abstract = "The standard 5-point difference scheme for the model problem Δu=f on a special polygonal domain with given boundary values is modified at a few points in the neighbourhood of the corners in such a way that the order of convergence at interior points is the same as in the case of a smooth boundary. As a side result improved error bounds for the usual method in the neighbourhood of corners are given.",

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AU - Zenger, C.

AU - Gietl, H.

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N2 - The standard 5-point difference scheme for the model problem Δu=f on a special polygonal domain with given boundary values is modified at a few points in the neighbourhood of the corners in such a way that the order of convergence at interior points is the same as in the case of a smooth boundary. As a side result improved error bounds for the usual method in the neighbourhood of corners are given.

AB - The standard 5-point difference scheme for the model problem Δu=f on a special polygonal domain with given boundary values is modified at a few points in the neighbourhood of the corners in such a way that the order of convergence at interior points is the same as in the case of a smooth boundary. As a side result improved error bounds for the usual method in the neighbourhood of corners are given.

KW - Subject Classifications: AMS(MOS):65N10, CR:5.17

UR - https://www.scopus.com/pages/publications/0013649053

U2 - 10.1007/BF01411846

DO - 10.1007/BF01411846

M3 - Article

AN - SCOPUS:0013649053

SN - 0029-599X

VL - 30

SP - 315

EP - 332

JO - Numerische Mathematik

JF - Numerische Mathematik

IS - 3

ER -

Improved difference schemes for the Dirichlet problem of Poisson's equation in the neighbourhood of corners

Abstract

Keywords

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