Multiscale Spectral Generalized Finite Element Methods for Discontinuous Galerkin Schemes

2025/10/24 by Christian Alber, Alber, Christian, Lukas Holbach +1
Computer Science · Engineering · #65N15 #65N30 #65N55 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Composite Material Mechanics #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2510.21289

openalex publication_date 2025/10/24 · openalex created_date 2025/10/28 · openalex updated_date 2026/07/28

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.

Citations

• A unified framework for multiscale spectral generalized FEMs and low-rank approximations to multiscale PDEs

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