Finite element approximation of the first eigenvalue of a nonlinear problem for some special domain

G. Bognár, University of Miskolc, Miskolc-Egyetemváros, Hungary

E. J. Qualitative Theory of Diff. Equ., Proc. 6'th Coll. Qualitative Theory of Diff. Equ., No. 1. (2000), pp. 1-12.

Abstract: In this paper we present a method for the numerical approximation of the smallest eigenvalue of a nonlinear eigenvalue problem using the finite element method. Numerical results are presented for some special domains when the domain is bounded by a square, a ''circle'', a ''semicircle'', or a quadrant of a ''circle''. We compare the exact solutions with the approximate solutions when the exact solutions are known. We show a connection among the first eigenvalues related to different domains.

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