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

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19 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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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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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

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JF - Numerische Mathematik

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ER -

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

Abstract

Keywords

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