An iteratively adaptive multiscale finite element method for elliptic interface problems

Feng Nan Hwang, Yi Zhen Su, Chien Chou Yao

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)211-225
Number of pages15
JournalApplied Numerical Mathematics
Volume127
DOIs
StatePublished - May 2018

Keywords

  • Adaptive multiscale finite element basis
  • Bubble functions
  • Elliptic interface problem
  • Multiscale problem

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