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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:223

Article

El-Gebeily, Mohamed A.¹  Furati, Khaled M.¹  O'Regan, Donal² 

[1] King Fahd Univ Petr & Minerals, Dept Math Sci, Dhahran 31261, Saudi Arabia

[2] Natl Univ Ireland, Dept Math, Galway, Ireland

关键词: Singular differential operators;    Self-adjoint operators;    Weak formulation;    Finite element method;    Galerkin method;   

DOI  :  10.1016/j.cam.2008.02.011

来源: Elsevier

【 摘 要 】

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. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

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