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arXiv · 2510.21289

Multiscale Spectral Generalized Finite Element Methods for Discontinuous Galerkin Schemes

Christian Alber·Lukas Holbach
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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.

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Christian Alber, Lukas Holbach. 2025-10-24. Multiscale Spectral Generalized Finite Element Methods for Discontinuous Galerkin Schemes. https://arxiv.org/abs/2510.21289

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