High-order multiscale finite element method for elliptic problems
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 650-666 |
| Journal / Publication | Multiscale Modeling and Simulation |
| Volume | 12 |
| Issue number | 2 |
| Online published | 22 May 2014 |
| Publication status | Published - 2014 |
Link(s)
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. © 2014 Society for Industrial and Applied Mathematics.
Research Area(s)
- Highorder accuracy, Multiscale finite element method, Oversampling, Petrov-galerkin, Scalar elliptic partial differential equation
Citation Format(s)
High-order multiscale finite element method for elliptic problems. / Hesthaven, Jan S.; Zhang, Shun; Zhu, Xueyu.
In: Multiscale Modeling and Simulation, Vol. 12, No. 2, 2014, p. 650-666.
In: Multiscale Modeling and Simulation, Vol. 12, No. 2, 2014, p. 650-666.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
