Journal article
High-Order Multiscale Finite Element Method for Elliptic Problems
Multiscale modeling & simulation, Vol.12(2), pp.650-666
01/01/2014
DOI: 10.1137/120898024
Abstract
In this paper, a new high-order multiscale finite element method (MsFEM) is developed for elliptic problems with highly oscillating coefficients. The method is inspired by the MsFEM developed in [G. Allaire and R. Brizzi, Multiscale Model. Simul., 4 (2005), pp. 790-812], but a more explicit multiscale finite element space is constructed. The approximation space is nonconforming when an oversampling technique is used. We use a Petrov-Galerkin formulation suggested in [T. Y. Hou, X.-H. Wu, and Y. Zhang, Commun. Math. Sci., 2 (2004), pp. 185-205] to simplify the implementation and to improve the accuracy. The method is natural for high-order finite element methods used with the advantage of solving the coarse grained problem. We prove optimal error estimates in the case of periodically oscillating coefficients and support the findings by various numerical experiments.
Details
- Title: Subtitle
- High-Order Multiscale Finite Element Method for Elliptic Problems
- Creators
- Jan S Hesthaven - Ecole Polytech Fed Lausanne, Math Inst Computat Sci & Engn MATHICSE, Chair Computat Math & Simulat Sci MCSS, CH-1015 Lausanne, SwitzerlandShun Zhang - City Univ Hong Kong, Dept Math, Kowloon Tong, Hong Kong, Peoples R ChinaXueyu Zhu
- Resource Type
- Journal article
- Publication Details
- Multiscale modeling & simulation, Vol.12(2), pp.650-666
- DOI
- 10.1137/120898024
- ISSN
- 1540-3459
- eISSN
- 1540-3467
- Publisher
- SIAM PUBLICATIONS
- Number of pages
- 17
- Grant note
- FA9550-09-1-0613 / OSD/AFOSR
- Language
- English
- Date published
- 01/01/2014
- Academic Unit
- Mathematics
- Record Identifier
- 9984240765602771
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