| Issue |
ESAIM: M2AN
Volume 59, Number 2, March-April 2025
|
|
|---|---|---|
| Page(s) | 1213 - 1237 | |
| DOI | https://doi.org/10.1051/m2an/2025029 | |
| Published online | 25 April 2025 | |
A localized orthogonal decomposition strategy for hybrid discontinuous Galerkin methods
1
Department of Mathematics Sciences, Soochow University, Suzhou 215006, P.R. China
2
Institute for Applied and Numerical Mathematics, Karlsruhe Institute of Technology, Englerstr. 2, 76131 Karlsruhe, Germany
3
Department of Mathematics, Saarland University, 66123 Saarbrücken, Germany
* Corresponding author: roland.maier@kit.edu
Received:
10
July
2024
Accepted:
3
April
2025
We formulate and analyze a multiscale method for an elliptic problem with an oscillatory coefficient based on a skeletal (hybrid) formulation. More precisely, we employ hybrid discontinuous Galerkin approaches and combine them with the localized orthogonal decomposition methodology to obtain a coarse-scale skeletal method that effectively includes fine-scale information. This work is the first step in reliably merging hybrid skeletal formulations and localized orthogonal decomposition to unite the advantages of both strategies. Numerical experiments are presented to illustrate the theoretical findings.
Mathematics Subject Classification: 65N12 / 65N30
Key words: Multiscale method / hybrid method / elliptic problems / Poincaré–Friedrichs inequalities for DG and HDG
© The authors. Published by EDP Sciences, SMAI 2025
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