Edge Multiscale Methods for elliptic problems with heterogeneous coefficients
For computational scientists solving multiscale PDEs, this provides new methods with theoretical convergence guarantees, though it is an incremental extension of existing multiscale frameworks.
The paper proposes two new edge multiscale methods (ESMsFEM and WEMsFEM) for solving elliptic PDEs with high-contrast heterogeneous coefficients, and proves their convergence rates in terms of mesh size, spectral basis count, and wavelet level, verified by numerical tests.
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.