Liliana Camargo, Manuel Solano:
A high order unfitted HDG method for the Helmholtz equation with first order absorbing boundary condition
This work analyzes a high order unfitted hybridizable discontinuous Galerkin (HDG) method for the Helmholtz equation in a non-polyhedral domain Ω with first order absorbing boundary condition. The HDG method is posed in a polyhedral subdomain Ωh whose boundary is at a distance δ from the boundary of Ω. The absorbing boundary data is properly transferred from ∂Ω to ∂Ωh in such a way that the method achieves high order accuracy. We first derive a stability analysis and then obtain the corresponding a priori error estimates, with the explicit dependence on the wavenumber κ, the meshsize h, the distance between the boundaries δ and the stabilization parameter of the method. Finally, the theoretical rates of convergence are supported by numerical experiments.