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数値解析セミナー
過去の記録 ～04/19｜次回の予定｜今後の予定 04/20～
| 開催情報 | 火曜日 16:30～18:00 数理科学研究科棟(駒場) 002号室 |
|---|---|
| 担当者 | 齊藤宣一、柏原崇人 |
| セミナーURL | https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/ |
2019年12月16日(月)
16:50-18:20 数理科学研究科棟(駒場) 117号室
上田祐暉 氏 (The Hong Kong Polytechnic University)
A second-order stabilization method for linearizing and decoupling nonlinear parabolic systems (Japanese)
上田祐暉 氏 (The Hong Kong Polytechnic University)
A second-order stabilization method for linearizing and decoupling nonlinear parabolic systems (Japanese)
[ 講演概要 ]
We present a new time discretization method for strongly nonlinear parabolic systems. Our method is based on backward finite difference for the first derivative with second-order accuracy and the first-order linear discrete-time scheme for nonlinear systems which has been introduced by H. Murakawa. We propose a second-order stabilization method by combining these schemes.
Our error estimate requires testing the error equation by two test functions and showing $W^{1,\infty}$-boundedness which is proved by ($H^2$ or) $H^3$ energy estimate. We overcome the difficulty for establishing energy estimate by using the generating function technique which is popular in studying ordinary differential equations. Several numerical examples are provided to support the theoretical result.
We present a new time discretization method for strongly nonlinear parabolic systems. Our method is based on backward finite difference for the first derivative with second-order accuracy and the first-order linear discrete-time scheme for nonlinear systems which has been introduced by H. Murakawa. We propose a second-order stabilization method by combining these schemes.
Our error estimate requires testing the error equation by two test functions and showing $W^{1,\infty}$-boundedness which is proved by ($H^2$ or) $H^3$ energy estimate. We overcome the difficulty for establishing energy estimate by using the generating function technique which is popular in studying ordinary differential equations. Several numerical examples are provided to support the theoretical result.
