Volume 5, Issue 5
Numerical Investigation on the Boundary Conditions for the Multiscale Base Functions

Shan Jiang & Yunqing Huang

DOI:

Commun. Comput. Phys., 5 (2009), pp. 928-941.

Published online: 2009-05

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  • Abstract

We study the multiscale finite element method for solving multiscale elliptic problems with highly oscillating coefficients, which is designed to accurately capture the large scale behaviors of the solution without resolving the small scale characters. The key idea is to construct the multiscale base functions in the local partial differential equation with proper boundary conditions. The boundary conditions are chosen to extract more accurate boundary information in the local problem. We consider periodic and non-periodic coefficients with linear and oscillatory boundary conditions for the base functions. Numerical examples will be provided to demonstrate the effectiveness of the proposed multiscale finite element method.

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@Article{CiCP-5-928, author = {}, title = {Numerical Investigation on the Boundary Conditions for the Multiscale Base Functions}, journal = {Communications in Computational Physics}, year = {2009}, volume = {5}, number = {5}, pages = {928--941}, abstract = {

We study the multiscale finite element method for solving multiscale elliptic problems with highly oscillating coefficients, which is designed to accurately capture the large scale behaviors of the solution without resolving the small scale characters. The key idea is to construct the multiscale base functions in the local partial differential equation with proper boundary conditions. The boundary conditions are chosen to extract more accurate boundary information in the local problem. We consider periodic and non-periodic coefficients with linear and oscillatory boundary conditions for the base functions. Numerical examples will be provided to demonstrate the effectiveness of the proposed multiscale finite element method.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7771.html} }
TY - JOUR T1 - Numerical Investigation on the Boundary Conditions for the Multiscale Base Functions JO - Communications in Computational Physics VL - 5 SP - 928 EP - 941 PY - 2009 DA - 2009/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7771.html KW - AB -

We study the multiscale finite element method for solving multiscale elliptic problems with highly oscillating coefficients, which is designed to accurately capture the large scale behaviors of the solution without resolving the small scale characters. The key idea is to construct the multiscale base functions in the local partial differential equation with proper boundary conditions. The boundary conditions are chosen to extract more accurate boundary information in the local problem. We consider periodic and non-periodic coefficients with linear and oscillatory boundary conditions for the base functions. Numerical examples will be provided to demonstrate the effectiveness of the proposed multiscale finite element method.

Shan Jiang & Yunqing Huang. (2020). Numerical Investigation on the Boundary Conditions for the Multiscale Base Functions. Communications in Computational Physics. 5 (5). 928-941. doi:
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