1. Edge multiscale methods for elliptic problems with heterogeneous coefficients.
- Author
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Fu, Shubin, Chung, Eric, and Li, Guanglian
- Subjects
- *
FINITE element method , *PARTIAL differential equations , *WAVELETS (Mathematics) , *EDGES (Geometry) - Abstract
In this paper, we proposed two new types of edge multiscale methods motivated by [14] to solve Partial Differential Equations (PDEs) with high-contrast heterogeneous coefficients: Edge Spectral Multiscale Finite 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 ℓ , which are verified by extensive numerical tests. • We propose a new multiscale methods for problems with heterogeneous coefficients. • This new approach is very accurate and efficient. • We apply the approximation properties of the wavelets on the edges. • This new approach is very flexible and can be applied to other problems. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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