The finite element-Galerkin method for singular self-adjoint differential equations

Mohamed A. El-Gebeily; Khaled M. Furati; Donal O'Regan

doi:10.1016/j.cam.2008.02.011

The finite element-Galerkin method for singular self-adjoint differential equations

Mohamed A. El-Gebeily^*, Khaled M. Furati, Donal O'Regan

^*Corresponding author for this work

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

2 Scopus citations

Abstract

We investigate the finite element-Galerkin method for singular self-adjoint second-order differential expressions. The weak formulation of the problem involves integration by parts, which allows the use of the usual piecewise linear functions. Our analysis shows that the method produces the solution corresponding to a particular self-adjoint realization of the differential expression. We also propose two algorithms to approximate the solution of any self-adjoint realization. Numerical examples are given to illustrate the analysis as well as the proposed algorithms.

Original language	English
Pages (from-to)	735-752
Number of pages	18
Journal	Journal of Computational and Applied Mathematics
Volume	223
Issue number	2
DOIs	https://doi.org/10.1016/j.cam.2008.02.011
State	Published - 15 Jan 2009

Bibliographical note

Funding Information:
We would like to thank the referee for many suggestions which led to improvements in the paper. Research of the first two authors has been funded by King Fahd University of Petroleum and Minerals under Project number MS/Singular ODE/274.

Keywords

Finite element method
Galerkin method
Self-adjoint operators
Singular differential operators
Weak formulation

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2008.02.011

Cite this

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title = "The finite element-Galerkin method for singular self-adjoint differential equations",

abstract = "We investigate the finite element-Galerkin method for singular self-adjoint second-order differential expressions. The weak formulation of the problem involves integration by parts, which allows the use of the usual piecewise linear functions. Our analysis shows that the method produces the solution corresponding to a particular self-adjoint realization of the differential expression. We also propose two algorithms to approximate the solution of any self-adjoint realization. Numerical examples are given to illustrate the analysis as well as the proposed algorithms.",

keywords = "Finite element method, Galerkin method, Self-adjoint operators, Singular differential operators, Weak formulation",

author = "El-Gebeily, \{Mohamed A.\} and Furati, \{Khaled M.\} and Donal O'Regan",

note = "Funding Information: We would like to thank the referee for many suggestions which led to improvements in the paper. Research of the first two authors has been funded by King Fahd University of Petroleum and Minerals under Project number MS/Singular ODE/274.",

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AU - El-Gebeily, Mohamed A.

AU - Furati, Khaled M.

AU - O'Regan, Donal

N1 - Funding Information: We would like to thank the referee for many suggestions which led to improvements in the paper. Research of the first two authors has been funded by King Fahd University of Petroleum and Minerals under Project number MS/Singular ODE/274.

PY - 2009/1/15

Y1 - 2009/1/15

N2 - We investigate the finite element-Galerkin method for singular self-adjoint second-order differential expressions. The weak formulation of the problem involves integration by parts, which allows the use of the usual piecewise linear functions. Our analysis shows that the method produces the solution corresponding to a particular self-adjoint realization of the differential expression. We also propose two algorithms to approximate the solution of any self-adjoint realization. Numerical examples are given to illustrate the analysis as well as the proposed algorithms.

AB - We investigate the finite element-Galerkin method for singular self-adjoint second-order differential expressions. The weak formulation of the problem involves integration by parts, which allows the use of the usual piecewise linear functions. Our analysis shows that the method produces the solution corresponding to a particular self-adjoint realization of the differential expression. We also propose two algorithms to approximate the solution of any self-adjoint realization. Numerical examples are given to illustrate the analysis as well as the proposed algorithms.

KW - Finite element method

KW - Galerkin method

KW - Self-adjoint operators

KW - Singular differential operators

KW - Weak formulation

UR - https://www.scopus.com/pages/publications/56949094306

U2 - 10.1016/j.cam.2008.02.011

DO - 10.1016/j.cam.2008.02.011

M3 - Article

AN - SCOPUS:56949094306

SN - 0377-0427

VL - 223

SP - 735

EP - 752

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 2

ER -

The finite element-Galerkin method for singular self-adjoint differential equations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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