A Finite-Element Method for Laplace- and Helmholtz-Type Boundary Value Problems with Singularities

Xiaonan Wu; Houde Han

doi:10.1137/s0036142993258488

A Finite-Element Method for Laplace- and Helmholtz-Type Boundary Value Problems with Singularities

Xiaonan Wu^*
, Houde Han

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

38 Citations (Scopus)

30 Downloads (Pure)

Abstract

Laplace- and Helmholtz-type boundary value problems with singularities are considered. A sequence of approximations to the exact boundary conditions at an artificial boundary is given. Then the original problem is reduced to a boundary value problem in a domain away from the singularities. Furthermore, finite-element approximations are applied to this problem and error estimates are obtained. Finally, some numerical examples show the effectiveness of this method.

Original language	English
Pages (from-to)	1037-1050
Number of pages	14
Journal	SIAM Journal on Numerical Analysis
Volume	34
Issue number	3
DOIs	https://doi.org/10.1137/s0036142993258488
Publication status	Published - May 1997

User-Defined Keywords

Approximate boundary conditions at an artificial boundary
Artificial boundary
Singularity

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title = "A Finite-Element Method for Laplace- and Helmholtz-Type Boundary Value Problems with Singularities",

abstract = "Laplace- and Helmholtz-type boundary value problems with singularities are considered. A sequence of approximations to the exact boundary conditions at an artificial boundary is given. Then the original problem is reduced to a boundary value problem in a domain away from the singularities. Furthermore, finite-element approximations are applied to this problem and error estimates are obtained. Finally, some numerical examples show the effectiveness of this method.",

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AU - Wu, Xiaonan

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N1 - Funding information: This work was supported in part by an FRG grant of Hong Kong Baptist University and the Doctoral Program Foundation of the Institute of Higher Education of China. Publisher copyright: Copyright © 1997 Society for Industrial and Applied Mathematics

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N2 - Laplace- and Helmholtz-type boundary value problems with singularities are considered. A sequence of approximations to the exact boundary conditions at an artificial boundary is given. Then the original problem is reduced to a boundary value problem in a domain away from the singularities. Furthermore, finite-element approximations are applied to this problem and error estimates are obtained. Finally, some numerical examples show the effectiveness of this method.

AB - Laplace- and Helmholtz-type boundary value problems with singularities are considered. A sequence of approximations to the exact boundary conditions at an artificial boundary is given. Then the original problem is reduced to a boundary value problem in a domain away from the singularities. Furthermore, finite-element approximations are applied to this problem and error estimates are obtained. Finally, some numerical examples show the effectiveness of this method.

KW - Approximate boundary conditions at an artificial boundary

KW - Artificial boundary

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A Finite-Element Method for Laplace- and Helmholtz-Type Boundary Value Problems with Singularities

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