Document Type


Publication Date



Particle size determination, Finite element method, Helmholtz equation, Galerkin 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.


This is the author’s version of a work that was accepted for publication in the Journal of Scientific Computing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Scientific Computing, Volume 77, Issue 3, pp 1703–1735 and is available online at:



Persistent Identifier

Included in

Mathematics Commons