| Issue |
ESAIM: M2AN
Volume 60, Number 3, May-June 2026
|
|
|---|---|---|
| Page(s) | 1135 - 1175 | |
| DOI | https://doi.org/10.1051/m2an/2026027 | |
| Published online | 01 June 2026 | |
Hybrid discontinuous Galerkin discretizations for the damped time-harmonic Galbrun’s equation
1
Institute for Applied and Numerical Mathematics, Karlsruhe Institute of Technology, Englerstraße 2, 76131, Karlsruhe, Germany
2
Institute for Numerical and Applied Mathematics, University of Göttingen, Lotzestr. 16-18, 37083, Göttingen, Germany
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
2
May
2025
Accepted:
21
March
2026
Abstract
In this article, we study the damped time-harmonic Galbrun's equation which models solar and stellar oscillations. We introduce and analyze hybrid discontinuous Galerkin discretizations (HDG) that are stable and optimally convergent for all polynomial degrees greater than or equal to one. The proposed methods are robust with respect to the drastic changes in the magnitude of the coefficients that naturally occur in stars. Our analysis is based on the concept of discrete approximation schemes and weak T-compatibility, which exploits the weakly T-coercive structure of the equation. Compared to the H1-conforming discretization of Halla et al. (2025), our method offers improved stability and robustness. Furthermore, it significantly reduces the computational costs compared to the H(div)-conforming DG discretization of Halla (2026), which has similar stability properties. These advantages make the proposed HDG methods well-suited for astrophysical simulations.
Mathematics Subject Classification: 65N12 / 65N30
Key words: Galbrun's equation / stellar oscillations / HDG methods / (weak) T-coercivity / T-compatibility / discrete approximation schemes
© The authors. Published by EDP Sciences, SMAI 2026
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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