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タイトル: | On the a posteriori estimates for inverse operators of linear parabolic equations with applications to the numerical enclosure of solutions for nonlinear problems |
著者: | Kinoshita, Takehiko Kimura, Takuma Nakao, Mitsuhiro T. |
著者名の別形: | 木下, 武彦 |
キーワード: | 35K20 65M15 65M60 |
発行日: | 1-Apr-2014 |
出版者: | Springer Berlin Heidelberg |
誌名: | Numerische Mathematik |
巻: | 126 |
号: | 4 |
開始ページ: | 679 |
終了ページ: | 701 |
抄録: | We consider the guaranteed a posteriori estimates for the inverse parabolic operators with homogeneous initial-boundary conditions. Our estimation technique uses a full-discrete numerical scheme, which is based on the Galerkin method with an interpolation in time by using the fundamental solution for semidiscretization in space. In our technique, the constructive a priori error estimates for a full discretization of solutions for the heat equation play an essential role. Combining these estimates with an argument for the discretized inverse operator and a contraction property of the Newton-type formulation, we derive an a posteriori estimate of the norm for the infinite-dimensional operator. In numerical examples, we show that the proposed method should be more efficient than the existing method. Moreover, as an application, we give some prototype results for numerical verification of solutions of nonlinear parabolic problems, which confirm the actual usefulness of our technique. |
著作権等: | © The Author(s) 2013. This article is published with open access at Springerlink.com |
URI: | http://hdl.handle.net/2433/187149 |
DOI(出版社版): | 10.1007/s00211-013-0575-z |
出現コレクション: | 学術雑誌掲載論文等 |
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