A Hybridizable Discontinuous Galerkin Method for the Helmholtz Equation with High Wave Number

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 u...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Chen, Huangxin, Lu, Peipei, Xu, Xuejun
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext bestellen
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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 $\kappa$. By exploiting the stability estimates, the dependence of convergence of the HDG method on $\kappa,h$ and $p$ is obtained. Numerical experiments are given to verify the theoretical results.
DOI:10.48550/arxiv.1207.3419