Simulation of a nonlinear Steklov eigenvalue problem using finite-element approximation

被引：0
作者：
Kumar P. [1 ,2 ]
Kumar M. [1 ,2 ]
机构：
[1] Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad
[2] Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad
来源：
Computational Mathematics and Modeling | 2010年 / 21卷 / 1期
关键词：
Weak Formulation; Elliptic Problem; Test Space; Steklov Eigenvalue; Steklov Problem;
D O I：
10.1007/s10598-010-9058-6
中图分类号：
学科分类号：
摘要：
Elliptic problems with parameters in the boundary conditions are called Steklov problems. With the tool of computational approximation (finite-element method), we estimate the solution of a nonlinear Steklov eigenvalue problem for a second-order, self-adjoint, elliptic differential problem. We discussed the behavior of the nonlinear problem with the help of computational results using Matlab. © 2010 Springer Science+Business Media, Inc.
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页码：109 / 116
页数：7
相关论文
共 14 条
[1]  
Canavati J., Minsoni A., A discontinuous Steklov problem with an application to water waves, J. Math. Anal. Appl., 69, pp. 540-558, (1979)
[2]  
Hinton D.B., Shaw J.K., Differential operators with spectral parameter incompletely in the boundary conditions, Funkcialaj Ekvacioj (Serio Internacia), 33, pp. 363-385, (1990)
[3]  
Ahn H.J., Vibration of a pendulum consisting of a bob suspended from a wire, Quart. Appl. Math., 39, pp. 109-117, (1981)
[4]  
Kuttler J.R., Sigillito V.G., Inequalities for membrane and Stekloff eigenvalues, J. Math. Anal. Appl., 23, pp. 148-160, (1968)
[5]  
Payne L.E., Some isoperimetric inequalities for harmonic functions, SIAM J. Math. Anal., 1, pp. 354-359, (1970)
[6]  
Ferrero A., Gazzola F., Weth T., On a fourth order Steklov eigenvalue problem, Analysis, 25, pp. 315-332, (2005)
[7]  
Bramble J.H., Osborn J.E., Approximation of Steklov eigenvalues of non-selfadjoint second-order elliptic operators, Math. Foundations of the Finite-Element Method with Applications to PDE, pp. 387-408, (1972)
[8]  
Andreev A.B., Hristov A.H., On the variational aspects for elliptic problems with parameter on the boundary, Recent Advances in Numerical Methods and Applications II, pp. 587-593, (1998)
[9]  
Babuska I., Osborn J., Eigenvalue Problem. Handbook of Numerical Analysis Vol. II, (1991)
[10]  
Bermudez A., Duran R., Rodriguez R., Finite-element solution of incompressible fluid-structure vibration problems, Internat. J. Numer. Meth. Eng., 40, pp. 1435-1448, (1997)
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