Help Privacy Policy Disclaimer
  Advanced SearchBrowse




Journal Article

A Hybridizable Discontinuous Galerkin Method for Steady-State Convection-Diffusion-Reaction Problems


Restelli,  Marco
The Ocean in the Earth System, MPI for Meteorology, Max Planck Society;

External Resource
No external resources are shared
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)
There are no public fulltexts stored in PuRe
Supplementary Material (public)
There is no public supplementary material available

Cockburn, B., Dong, B., Guzman, J., Restelli, M., & Sacco, R. (2009). A Hybridizable Discontinuous Galerkin Method for Steady-State Convection-Diffusion-Reaction Problems. SIAM Journal on Scientific Computing, 31, 3827-3846. doi:10.1137/080728810.

Cite as: https://hdl.handle.net/21.11116/0000-000B-4E65-D
In this article, we propose a novel discontinuous Galerkin method for convection-diffusion-reaction problems, characterized by three main properties. The first is that the method is hybridizable; this renders it efficiently implementable and competitive with the main existing methods for these problems. The second is that, when the method uses polynomial approximations of the same degree for both the total flux and the scalar variable, optimal convergence properties are obtained for both variables; this is in sharp contrast with all other discontinuous methods for this problem. The third is that the method exhibits superconvergence properties of the approximation to the scalar variable; this allows us to postprocess the approximation in an element-by-element fashion to obtain another approximation to the scalar variable which converges faster than the original one. In this paper, we focus on the efficient implementation of the method and on the validation of its computational performance. With this aim, extensive numerical tests are devoted to explore the convergence properties of the novel scheme, to compare it with other methods in the diffusion-dominated regime, and to display its stability and accuracy in the convection-dominated case.