Staggered discontinuous Galerkin methods for the Helmholtz equation with large wave number

Abstract

In this paper we investigate staggered discontinuous Galerkin method for the Helmholtz equation with large wave number on general polygonal meshes. The method is highly flexible by allowing rough grids such as the trapezoidal grids and highly distorted grids, and at the same time, is numerical flux free. Furthermore, it allows hanging nodes, which can be simply treated as additional vertices. By exploiting a modified duality argument, the stability and convergence can be proved under the condition that κh≤C0(1κ)1m+1, where m is the polynomial order, κ is the wave number, h is the mesh size and C0 is a positive constant independent of κ,h. Error estimates for both the scalar and vector variables in L2 norm are established. Several numerical experiments are tested to verify our theoretical results and to present the capability of our method for capturing singular solutions.