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Removing the Cell Resonance Error in the Multiscale Finite Element Method via a Petrov-Galerkin Formulation
| Content Provider | Semantic Scholar |
|---|---|
| Author | Hou, Thomas Y. Wu, Xiao-Hui Zhang, Yu |
| Copyright Year | 2004 |
| Abstract | We continue the study of the nonconforming multiscale finite element method (Ms- FEM) introduced in 17, 14 for second order elliptic equations with highly oscillatory coefficients. The main difficulty in MsFEM, as well as other numerical upscaling methods, is the scale resonance effect. It has been show that the leading order resonance error can be effectively removed by using an over-sampling technique. Nonetheless, there is still a secondary cell resonance error of O(Є^2/h^2). Here, we introduce a Petrov-Galerkin MsFEM formulation with nonconforming multiscale trial functions and linear test functions. We show that the cell resonance error is eliminated in this formulation and hence the convergence rate is greatly improved. Moreover, we show that a similar formulation can be used to enhance the convergence of an immersed-interface finite element method for elliptic interface problems. |
| Starting Page | 185 |
| Ending Page | 205 |
| Page Count | 21 |
| File Format | PDF HTM / HTML |
| DOI | 10.4310/CMS.2004.v2.n2.a3 |
| Volume Number | 2 |
| Alternate Webpage(s) | http://users.cms.caltech.edu/~hou/papers/Hou_Wu_Zhang.pdf |
| Alternate Webpage(s) | http://users.cms.caltech.edu/~hou/papers/MsFEM_cell.pdf |
| Alternate Webpage(s) | http://www.ama.caltech.edu/~hou/papers/Hou_Wu_Zhang.pdf |
| Alternate Webpage(s) | http://www.ama.caltech.edu/~hou/papers/MsFEM_cell.pdf |
| Alternate Webpage(s) | https://doi.org/10.4310/CMS.2004.v2.n2.a3 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
