A Hybridizable Weak Galerkin Method for the Helmholtz Equation with Large Wave Number: $hp$ Analysis

Abstract

In this paper, an $hp$ hybridizable weak Galerkin ($hp$-HWG) method is introduced to solve the Helmholtz equation with large wave number in two and three dimensions. By choosing a specific parameter and using the duality argument, we prove that the proposed method is stable under certain mesh constraint. Error estimate is obtained by using the stability analysis and the duality argument. Several numerical results are provided to confirm our theoretical results.