SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1394-1419, June 2024.
Abstract. In this paper, we analyze a hybridizable discontinuous Galerkin method for the Helmholtz equation with large wave number, which uses piecewise polynomials of degree of [math] to approximate the potential [math] and its traces and piecewise polynomials of degree of [math] for the flux [math]. It is proved that [math] and [math] hold under the conditions that [math] is sufficiently small and that the penalty parameter [math], where [math] is the mesh size. Numerical experiments are proposed to verify our theoretical findings and to show that the pollution error may be greatly reduced by tuning the penalty parameter.

中文翻译：

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大波数亥姆霍兹方程的([math],[math])-HDG方法


《SIAM 数值分析杂志》，第 62 卷，第 3 期，第 1394-1419 页，2024 年 6 月。

抽象的。在本文中，我们分析了大波数亥姆霍兹方程的可混合间断伽辽金方法，该方法使用[math]次数的分段多项式来逼近势[math]及其迹以及[math]次数的分段多项式通量[数学]。证明了[math]和[math]在[math]足够小且惩罚参数[math]成立的条件下成立，其中[math]是网格尺寸。提出了数值实验来验证我们的理论结果，并表明通过调整惩罚参数可以大大减少污染误差。