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An iteratively adaptive multiscale finite element method for elliptic interface problems

Authors :
Feng Nan Hwang
Chien Chou Yao
Yi Zhen Su
Source :
Applied Numerical Mathematics. 127:211-225
Publication Year :
2018
Publisher :
Elsevier BV, 2018.

Abstract

We develop and study a framework of multiscale finite element method (MsFEM) for solving the elliptic interface problems. Finding an appropriate boundary condition setting for local multiscale basis function problems is the current topic in the MsFEM research. In the proposed framework, which we call the iteratively adaptive MsFEM (i-ApMsFEM), the local-global information exchanges through iteratively updating the local boundary condition. Once the multiscale solution is recovered from the solution of global numerical formulation on coarse grids, which couples these multiscale basis functions, it provides feedback for updating the local boundary conditions on each coarse element. The key step of i-ApMsFEM is to perform a few smoothing iterations for the multiscale solution to eliminate the high-frequency error introduced by the inaccurate coarse solution before it is used for setting the boundary condition. As the method iterates, the quality of the MsFEM solution improves, since these adaptive basis functions are expected to capture the multiscale feature of the approximate solution more accurately. We demonstrate the advantage of the proposed method through some numerical examples for elliptic interface benchmark problems.

Details

ISSN :
01689274
Volume :
127
Database :
OpenAIRE
Journal :
Applied Numerical Mathematics
Accession number :
edsair.doi...........d95a7da1dd51f4a7a1d23cf6be13a8ec
Full Text :
https://doi.org/10.1016/j.apnum.2018.01.009