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arXiv · 1810.10398

Edge Multiscale Methods for elliptic problems with heterogeneous coefficients

Shubin Fu·Eric Chung·Guanglian Li
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Abstract

In this paper, we proposed two new types of edge multiscale methods motivated by \cite{GL18} to solve Partial Differential Equations (PDEs) with high-contrast heterogeneous coefficients: Edge spectral multiscale Finte Element method (ESMsFEM) and Wavelet-based edge multiscale Finite Element method (WEMsFEM). Their convergence rates for elliptic problems with high-contrast heterogeneous coefficients are demonstrated in terms of the coarse mesh size $H$, the number of spectral basis functions and the level of the wavelet space $\ell$, which are verified by extensive numerical tests.

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Shubin Fu, Eric Chung, Guanglian Li. 2018-10-24. Edge Multiscale Methods for elliptic problems with heterogeneous coefficients. https://doi.org/10.1016/j.jcp.2019.06.006

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