Finite element method for a nonlinear problem

  • Gabriella Bognar University of Miskolc

Abstract

We consider the nonlinear eigenvalue problem of a nonlinear partial differential equation under Dirichlet boundary condition in a two-dimensional space. The classical solutions are given for rectangular domains. We give numerical solutions obtained by finite element method for the first eigenvalue and eigenfunctions and we analyze the error in the approximate finite element solutions.

Keywords

References

[l] G. Bognar. On the solution of some nonlinear boundary value problem. Proc. WCNA, August 19- 26, 1992. Tampa, Florida, 2449- 2458, 1992.
[2] G. Bognar. Existence theorem for eigenvalues of a nonlinear eigenvalue problem. Communications on Applied Nonlinear Analysis, 4(2): 93- 102, 1997.
[3] G. Bognar. Error estimates for the finite element solution of a nonlinear elliptic problem. J. of Nonlin. Anal. (to appear)
[4] P.G. Ciarlet. The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam- New York- Oxford, 1979.
[5] A. Elbert. A half-linear second order differential equation, Coli. Math. Soc. Janos Bolyai, 30. Qualitative theory of differential equations, 153- 179. Szeged, 1979.
Published
Mar 29, 2023
How to Cite
BOGNAR, Gabriella. Finite element method for a nonlinear problem. Computer Assisted Methods in Engineering and Science, [S.l.], v. 7, n. 4, p. 471-478, mar. 2023. ISSN 2956-5839. Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/1204>. Date accessed: 23 dec. 2024.
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Vol 7 No 4 (2000)
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Articles
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