Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications
2012
Session Number:D1L-D
Session:
Number:816
A computer-assisted proof method of the invertibility to elliptic operators
Akitoshi Takayasu, Shin'ichi Oishi,
pp.816-819
Publication Date:
Online ISSN:2188-5079
[1] L.V. Kantorovich and G.P. Akilov. Functional analysis in normed spaces. International series of monographs in pure and applied mathematics. Pergamon Press, 1964.
[2] M. Plum. Explicit H2-estimates and pointwise bounds for solutions of second-order elliptic boundary value problems, Journal of Mathematical Analysis and Applications, 165, (1992) pp.36-61.
[3] M.T. Nakao, K. Hashimoto, and Y. Watanabe. A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems. Computing, 75(1), pp.1-14, 2005.
[4] X. Liu and S. Oishi. Verified eigenvalue evaluation for elliptic operator on arbitrary polygonal domain. in preparation.
[5] S.M. Rump. INTLAB-INTerval LABoratory. In Tibor Csendes, editor, Developments in Reliable Computing, pp. 77-104. Kluwer Academic Publishers, Dordrecht, 1999. http://www.ti3.tu-harburg.de/rump/.
[6] C. Geuzaine and J.-F. Remacle. Gmsh: A 3-d finite element mesh generator with built-in pre- and post-processing facilities. International Journal for Numerical Methods in Engineering, 79(11):1309-1331, 2009. http://www.geuz.org/gmsh/.