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Numerical verification method of solutions for elliptic equations and its application to the RayleighBénard problem
 Yoshitaka Watanabe,
 Mitsuhiro T. Nakao
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We first summarize the general concept of our verification method of solutions for elliptic equations. Next, as an application of our method, a survey and future works on the numerical verification method of solutions for heat convection problems known as RayleighBénard problem are described. We will give a method to verify the existence of bifurcating solutions of the twodimensional problem and the bifurcation point itself. Finally, an extension to the threedimensional case and future works will be described.
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 Title
 Numerical verification method of solutions for elliptic equations and its application to the RayleighBénard problem
 Journal

Japan Journal of Industrial and Applied Mathematics
Volume 26, Issue 23 , pp 443463
 Cover Date
 20091001
 DOI
 10.1007/BF03186543
 Print ISSN
 09167005
 Online ISSN
 1868937X
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 numerical verification method
 elliptic equations
 RayleighBénard problem
 bifurcation point
 Authors

 Yoshitaka Watanabe ^{(1)}
 Mitsuhiro T. Nakao ^{(2)}
 Author Affiliations

 1. Research Institute for Information Technology, Kyushu University, 6101 HigashiKu Hakozaki, 8128581, Fukuoka, Japan
 2. Faculty of Mathematics, Kyushu University, Japan