Validated Computation for a Linear Elliptic Problem with a Parameter

Nobito Yamamoto, Mitsuhiro T. Nakao and Yoshitaka Watanabe
Advances in Numerical Mathematics;
Proceedings of the Fourth Japan-China Joint Seminar on Numerical Mathematics, held in Chiba, Japan, August 24-28, 1998 (H. Kawarada, M. Nakamura, Z. Shi, eds.), GAKUTO International Series Mathematical Sciences and Applications, Volume 12, Gakkotosho, Tokyo, Japan (1999) pp.155-162.

This paper proposes an efficient method for validated computing of the solution of linear elliptic problem with a parameter. A numerical method to obtain the k-th eigenvalue of given symmetric matrices is also developed. This paper presents some numerical examples which concern with the problem to determine a constant appearing in error estimation of the Finite Element Method (FEM). 8 pages.

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