一些特殊退化二次橢圓算子的勻質化問題與計算

Homogenization of some special degenerate second order linear elliptic operators and its numerical computation

沈林弘(Lin-hong Shen)

指導教授 ： 朱家杰

國立清華大學/理學院/數學系/碩士(2014年)

https://doi.org/10.6843/NTHU.2014.00610

摘要

我們在這篇論文中討論了一些特殊退化二次橢圓算子的勻質化問題, 並利用有限元素法做了幾個數值上的計算

關鍵字

勻質化 ； 退化橢圓方程 ； 漸進行為 ； 數值分析

並列摘要

Abstract

Homogenization of some special degenerate second order linear elliptic operators and its numerical computation
Lin-Hong Shen, Avisor:Assistant Professor Chia-Chieh Chu
Department of Mathematics
National Tsing Hua University, Hsin-Chu City,Taiwan

In many area, homogenization is an alternative way to find out the asymptotic behaviour of partial differential equation. This arti- cle is about homogenization process of degenerate second order linear elliptic operators. In this article, we give both theoretical and com- putational analysis to the asymptotic behaviour of the solution of the equation.
−div(a( x )Duh) = f on Ω ,
uh |∂Ω= 0 on ∂Ω ,

when Eh tends to zero, where aij (x) is Y -periodic, nonnegative defi- nite for almost every x in domain Ω and vanishes at some points in Ω. We find out that the homogenization process of degenerate ellip- tic equation in rectangle domain is still available for some particular coefficient functions with its inverse is integrable
Key words: homogenization, degenerate elliptic equation, asymp- totic behaviour, numerical analysis

並列關鍵字

homogenization ； degenerate elliptic equation ； asymptotic behaviour ； numerical analysis

參考文獻

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