Finite element method for a nonlinear problem
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.
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.
[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
2023-03-29
Issue
pp. 471-478
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Bognar, G. (2023). Finite element method for a nonlinear problem. Computer Assisted Methods in Engineering and Science, 7(4), 471-478. https://cames3.ippt.pan.pl/index.php/cames/article/view/1204
