数値解析セミナー

過去の記録 ~12/10次回の予定今後の予定 12/11~

開催情報 火曜日 16:30~18:00 数理科学研究科棟(駒場) 056号室
担当者 齊藤宣一
セミナーURL http://www.infsup.jp/utnas/

2017年12月19日(火)

16:50-18:20   数理科学研究科棟(駒場) 128号室
三浦達彦 氏
Finite volume scheme for the Hamilton-Jacobi equation on an evolving surface (Japanese)
[ 講演概要 ]
In this talk we consider the first-order Hamilton-Jacobi equation on a given closed evolving surface embedded into the three-dimensional Euclidean space, which describes the motion of a closed curve on the evolving surface. Our aim is to give a numerical scheme and establish its convergence and an error estimate between numerical and viscosity solutions.
Based on a finite volume scheme for the Hamilton-Jacobi equation on a flat domain introduced by Kim and Li (J. Comput. Math., 2015), we construct a numerical scheme on triangulated surfaces and prove its monotonicity and consistency without assuming that the triangulation is acute. Then applying these results we show the convergence of a numerical solution to a viscosity solution and an error estimate of the same order as in the case of a flat stationary domain.
This talk is based on a joint work with Prof. Klaus Deckelnick (Otto von Guericke University Magdeburg) and Prof. Charles M. Elliott (University of Warwick).