Dispersion Analysis of HDG Methods
This work presents a dispersion analysis of the Hybrid Discontinuous Galerkin (HDG) method. Considering the Helmholtz system, we quantify the discrepancies between the exact and discrete wavenumbers. In particular, we obtain an analytic expansion for the wavenumber error for the lowest order Single Face HDG (SFH) method. The expansion shows that the SFH method exhibits convergence rates of the wavenumber errors comparable to that of the mixed hybrid Raviart–Thomas method. In addition, we observe the same behavior for the higher order cases in numerical experiments.
KeywordsDispersion analysis Hybridizable discontinuous Galerkin Helmholtz equation
This paper is the outgrowth of a suggestion from Prof. Bernardo Cockburn to go beyond the standard HDG method while comparing dispersion relations. On this occasion for celebrating Prof. Cockburn’s contributions, the authors would like to place on record their deep appreciation for his tireless efforts to nurture the mathematical community of researchers in discontinuous Galerkin methods over the years. This work was initiated while the student author F. Vargas was visiting Portland State University, thanks to the support from CONICYT, Chile. M. Solano was partially supported by Conicyt-Chile through Fondecyt project No. 1160320 and project AFB170001 of the PIA Program: Concurso Apoyo a Centros Científicos y Tecnológicos de Excelencia con Financiamiento Basal.