Local multiscale model reduction using discontinuous Galerkin coupling for elasticity problems

In this paper, we consider the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with discontinuous Galerkin (DG) coupling for the linear elasticity equations in highly heterogeneous and high contrast media. We will introduce the construction of a DG version of...

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Bibliographic Details
Published inarXiv.org
Main Authors Wang, Zhongqian, Fu, Shubin, Chung, Eric
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 10.10.2022
Subjects
Basis functions
Computer Science - Numerical Analysis
Contrast media
Coupling
Discrete systems
Elasticity
Finite element method
Galerkin method
Mathematical analysis
Mathematics - Mathematical Physics
Mathematics - Numerical Analysis
Model reduction
Physics - Mathematical Physics
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Summary:In this paper, we consider the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with discontinuous Galerkin (DG) coupling for the linear elasticity equations in highly heterogeneous and high contrast media. We will introduce the construction of a DG version of the CEM-GMsFEM, such as auxiliary basis functions and offline basis functions. The DG version of the method offers some advantages such as flexibility in coarse grid construction and sparsity of resulting discrete systems. Moreover, to our best knowledge, this is the first time where the proof of the convergence of the CEM-GMsFEM in the DG form is given. Some numerical examples will be presented to illustrate the performance of the method.
ISSN:2331-8422
DOI:10.48550/arxiv.2204.07723