Reduced basis finite element heterogeneous multiscale method for high-order discretizations of elliptic homogenization problems
نویسندگان
چکیده
منابع مشابه
Reduced basis finite element heterogeneous multiscale method for high-order discretizations of elliptic homogenization problems
A new finite element method for the efficient discretization of elliptic homogenization problems is proposed. These problems, characterized by data varying over a wide range of scales cannot be easily solved by classical numerical methods that need mesh resolution down to the finest scales and multiscale methods capable of capturing the large scale components of the solution on macroscopic mesh...
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A reduced basis finite element heterogeneous multiscale method (RB-FE-HMM) for a class of nonlinear homogenization elliptic problems of nonmonotone type is introduced. In this approach, the solutions of the micro problems needed to estimate the macroscopic data of the homogenized problem are selected by a Greedy algorithm and computed in an offline stage. It is shown that the use of reduced bas...
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In this paper, a new high-order multiscale finite element method is developed for elliptic problems with highly oscillating coefficients. The method is inspired by the multiscale finite element method developed in [3], but a more explicit multiscale finite element space is constructed. The approximation space is nonconforming when oversampling technique is used. We use a PetrovGalerkin formulat...
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Article history: Received 27 August 2009 Received in revised form 29 April 2010 Accepted 8 June 2010 Available online 18 June 2010
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JAN S. HESTHAVEN ∗, SHUN ZHANG † , AND XUEYU ZHU ‡ Abstract. In this paper, we propose reduced basis multiscale finite element methods (RB-MsFEM) for elliptic problems with highly oscillating coefficients. The method is based on multiscale finite element methods with local test functions that encode the oscillatory behavior ([4, 14]). For uniform rectangular meshes, the local oscillating test f...
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ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 2012
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2012.02.019