An HDG method for dissimilar meshes

Abstract

We present a hybridizable discontinuous Galerkin (HDG) method for dissimilar meshes. The method is devised by formulating HDG discretizations on separate meshes and gluing these HDG discretizations through appropriate transmission conditions that weakly enforce the continuity of the numerical trace and the numerical flux across the dissimilar interfaces. The transmission conditions are based upon transferring the numerical flux from the first mesh to the second mesh and the numerical trace from the second mesh to the first one. The transfer of the numerical trace/flux from one mesh to the other relies on the extrapolation of the approximate flux, and is made to be consistent with the HDG methodology for conforming meshes. Stability of the HDG method is shown and the error analysis of the HDG method is established. Numerical results are presented to validate the theoretical results.