Quantitative study of adaptive mesh FEM with localization index of pattern
Masato Kimura, 正人 木村, マサト キムラ, Hideki Komura, Hideki Komura, Masayasu Mimura, 昌泰 三村, マサヤス ミムラ, Hidenori Miyoshi, Hidenori Miyoshi, Takeshi Takaishi, 武史 高石, タケシ タカイシ, Daishin Ueyama, 大信 上山, Daishin Ueyama · Institutional Repositories DataBase (IRDB) · 2006
Abstract. We study the effectivity of an adaptive mesh algorithm with triangular finite elements for two or three dimensional pattern dynamics appearing in several reaction-diffusion systems. The aim of this paper is to investigate a relation between the effectivity of the adaptive mesh and the pattern profile through several numerical experiments. Based on the result of our previous paper [6], the effectivity of the adaptive mesh is estimated in terms of the compression rate of the adapted mesh. We introduce a quantity called localization index which characterizes pattern profiles of numerical solutions. Key words. Pattern dynamics, reaction-diffusion system, finite element method, adaptive mesh. AMS subject classifications. 35K57, 65M50, 65M60, 74S05 1. Introduction. The