Summary
2011 International Symposium on Nonlinear Theory and Its Applications
2011
Session Number:A2L-A
Session:
Number:A2L-A4
Computer assisted proofs for solutions to nonlinear elliptic partial differential equations on arbitrary polygonal domain
Akitoshi Takayasu, Xuefeng Liu, Shin’ichi Oishi,
pp.90-93
Publication Date:2011/9/4
Online ISSN:2188-5079
Summary:
In this article, a computer assisted proof framework is introduced. Computer assisted proof method shows the existence and local uniqueness of exact solutions of nonlinear PDEs. Based on Newton-Kantorovich theorem, our numerical method is another variant of computer assisted proofs which provides verified numerical error estimates by numerical computations with result verification. One feature is that, by adopting hyper-circle equation in a posteriori error estimate, our method can deal with ar- bitrary polygonal domain. Furthermore, Raviart-Thomas mixed finite element enables us to get an effective residual bounds with respect to an operator equation. Our approach is presented first for an abstract problem. Then, some numerical results are demonstrated.