标题： 混合间断Galerkin离散化在阻尼时谐Galbrun方程中的应用 显示英文标题

标题： Hybrid discontinuous Galerkin discretizations for the damped time-harmonic Galbrun's equation

摘要： 本文中，我们研究了阻尼时谐 Galbrun 方程，该方程用于模拟太阳和恒星的振荡。 我们引入并分析了混合间断伽辽金离散化（HDG）方法，这些方法对于所有大于或等于一的多项式次数都是稳定且最优收敛的。 所提出的方法对于恒星中自然出现的系数大小剧烈变化具有鲁棒性。 我们的分析基于离散逼近方案和弱 T-相容性的概念，利用了方程的弱 T-强制结构。 与 [Halla, Lehrenfeld, Stocker, 2022] 的$H^1$-连续离散化相比，我们的方法提供了更好的稳定性和鲁棒性。 此外，与 [Halla, 2023] 的具有相似稳定性特性的$H(\operatorname{div})$-连续 DG 离散化相比，它显著降低了计算成本。 这些优势使所提出的 HDG 方法非常适合天体物理模拟。 显示英文摘要

摘要： 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 $H^1$-conforming discretization of [Halla, Lehrenfeld, Stocker, 2022], our method offers improved stability and robustness. Furthermore, it significantly reduces the computational costs compared to the $H(\operatorname{div})$-conforming DG discretization of [Halla, 2023], which has similar stability properties. These advantages make the proposed HDG methods well-suited for astrophysical simulations.