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arXiv · 2210.11297

A multiscale method for inhomogeneous elastic problems with high contrast coefficients

Zhongqian Wang·Changqing Ye·Eric T. Chung
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Abstract

In this paper, we develop the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with mixed boundary conditions (Dirichlet and Neumann) for the elasticity equations in high contrast media. By a special treatment of mixed boundary conditions separately, and combining the construction of the relaxed and constraint version of the CEM-GMsFEM, we discover that the method offers some advantages such as the independence of the target region's contrast from precision, while the sizes of oversampling domains have a significant impact on numerical accuracy. Moreover, to our best knowledge, this is the first proof of the convergence of the CEM-GMsFEM with mixed boundary conditions for the elasticity equations given. Some numerical experiments are provided to demonstrate the method's performance.

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Zhongqian Wang, Changqing Ye, Eric T. Chung. 2022-10-20. A multiscale method for inhomogeneous elastic problems with high contrast coefficients. https://arxiv.org/abs/2210.11297

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