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

• Main Authors: Shen, Lin-hong, 沈林弘
• Other Authors: Chu, Chia-chieh
• Format: Others
• Language: zh-TW
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/09316679482569904004

碩士 === 國立清華大學 === 數學系 === 103 === 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