高波数亥姆霍兹方程的可混合不连续伽辽金方法
A Hybridizable Discontinuous Galerkin Method for the Helmholtz Equation with High Wave Number
AI总结：
本文分析可混合不连续伽辽金（HDG）方法求解高波数亥姆霍兹方程的误差估计，通过选择特定参数和对偶论证证明该方法在无网格约束下对任意波数稳定，并给出收敛性对波数、网格尺寸和多项式阶的依赖关系。
AI中文摘要：
本文分析了可混合不连续伽辽金（HDG）方法在二维和三维中求解高波数亥姆霍兹方程的误差估计。我们处理的分片多项式空间阶数为 $p\geq 1$。通过选择一个特定参数并使用对偶论证，证明了HDG方法对于任意波数 $κ$ 在没有任何网格约束的情况下是稳定的。利用稳定性估计，得到了HDG方法收敛性对 $κ,h$ 和 $p$ 的依赖关系。给出了数值实验来验证理论结果。
英文摘要：
This paper analyzes the error estimates of the hybridizable discontinuous Galerkin (HDG) method for the Helmholtz equation with high wave number in two and three dimensions. The approximation piecewise polynomial spaces we deal with are of order $p\geq 1$. Through choosing a specific parameter and using the duality argument, it is proved that the HDG method is stable without any mesh constraint for any wave number $κ$. By exploiting the stability estimates, the dependence of convergence of the HDG method on $κ,h$ and $p$ is obtained. Numerical experiments are given to verify the theoretical results.
