Ngoc-Cuong Nguyen, Jaime Peraire, Manuel Solano, Sébastien Terrana:
An HDG method for non-matching meshes
We present a hybridizable discontinuous Galerkin (HDG) method for non-matching meshes. The method is devised by formulating HDG discretizations on the non-matching 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 non-matching meshes. 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 mesh. The transfer of the numerical trace/flux from one mesh to the other mesh 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.
This preprint gave rise to the following definitive publication(s):
Ngoc-Cuong NGUYEN, Jaime PERAIRE, Manuel SOLANO, Sébastien TERRANA: An HDG method for dissimilar meshes. IMA Journal of Numerical Analysis, vol. 42, Issue 2, pp. 1665-1699, (2022).