Multiscale Spectral Generalized Finite Element Methods for Discontinuous Galerkin Schemes
Numerical Analysis
2026-01-15 v2 Numerical Analysis
Abstract
We propose a multiscale spectral generalized finite element method (MS-GFEM) for discontinuous Galerkin (DG) discretizations. The method builds local approximations on overlapping subdomains as the sum of a local source solution and a correction from an optimal spectral coarse space, which is obtained from a generalized eigenproblem. The global solution is then assembled via a partition of unity. We prove nearly exponential decay of the approximation error for second-order elliptic problems with highly heterogeneous diffusion discretized by a weighted symmetric interior-penalty DG scheme.
Cite
@article{arxiv.2510.21289,
title = {Multiscale Spectral Generalized Finite Element Methods for Discontinuous Galerkin Schemes},
author = {Christian Alber and Lukas Holbach},
journal= {arXiv preprint arXiv:2510.21289},
year = {2026}
}