TY - JOUR
T1 - High-order multiscale finite element method for elliptic problems
AU - Hesthaven, Jan S.
AU - Zhang, Shun
AU - Zhu, Xueyu
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
KW - Highorder accuracy
KW - Multiscale finite element method
KW - Oversampling
KW - Petrov-galerkin
KW - Scalar elliptic partial differential equation
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U2 - 10.1137/120898024
DO - 10.1137/120898024
M3 - 21_Publication in refereed journal
VL - 12
SP - 650
EP - 666
JO - Multiscale Modeling and Simulation
JF - Multiscale Modeling and Simulation
SN - 1540-3459
IS - 2
ER -