MultiScale Asymptotic Analysis Method with High Accuracy for the Second Order Elliptic Equation with Oscillating Periodic Coefficients in Perforated Domain

Author

Liu, Xiao-Qi ; Zhu, Qi-Ding

Author_Institution

Inst. of Math. & Phys., Central South Univ. of Forestry & Technol., Changsha, China

Volume

1

fYear

2009

fDate

7-8 Nov. 2009

Firstpage

225

Lastpage

230

Abstract

We consider the Neumman boundary value problem of second order elliptic equation with oscillating periodic coefficients in perforated domains. It is very difficult to solve the problem by using numerical methods directly, such as finite element method and finite difference method, due to the huge computing scaling. Using homogenization method, two-scale asymptotic expansion and projective interpolation, a high accuracy algorithm and its error estimate are reported. The rigorous proofs of the results are proposed. Finally, numerical example supports the theoretical results.

Keywords

boundary-value problems; finite difference methods; finite element analysis; interpolation; Neumman boundary value problem; asymptotic expansion; error estimate; finite difference method; finite element method; homogenization method; multiscale asymptotic analysis method; oscillating periodic coefficients; perforated domain; projective interpolation; second order elliptic equation; Artificial intelligence; Computational intelligence; Computer science; Educational institutions; Equations; Forestry; Interpolation; Mathematics; Physics; Space technology; asymptotic expansion; high accuracy; homogenization; multiscale; perforated domain; projective interpolation;

fLanguage

English

Publisher

ieee

Conference_Titel

Artificial Intelligence and Computational Intelligence, 2009. AICI '09. International Conference on

Conference_Location

Shanghai

Print_ISBN

978-1-4244-3835-8

Electronic_ISBN

978-0-7695-3816-7

Type

conf

DOI

10.1109/AICI.2009.452

Filename

5376105