| RWTH Publication No: 561901 2015   IGPM439.pdf
| A hierarchical scale separation approach for the hybridized discontinuous Galerkin method
|Jochen Schütz, Vadym Aizinger
|In this work, the hierarchical scale separation (HSS) method developed for linear systems resulting from discontinuous Galerkin (DG) discretizations has been extended to hybridized discontinuous Galerkin (HDG) schemes. The HSS method is related to p-multigrid techniques for DG systems but is conceptually much simpler. Our extension of the HSS scheme to the HDG method tested using a convection-diffusion equation for a range of benchmark problems demonstrated excellent performance on a par with that of the HSS method for a non-hybridized DG approximation. In the limiting case of a pure convection equation, the measured convergence rate of the HSS scheme was significantly better than the rates demonstrated in the non-hybridized case.
| hybridized discontinuous Galerkin method, hierarchical scale separation, convection-diffusion equation, p-multigrid method
| Journal of Computational and Applied Mathematics, Volume 317, June 2017, Pages 500-509