A hybrid discontinuous Galerkin (HDG) method for the Poisson problem introduced by Jeon and Park can be viewed as a hybridizable discontinuous Galerkin method using a Baumann-Oden type local solver. In this work, an upwind HDG method with super-penalty is proposed to solve advection-diffusion-reaction problems. A super-penalty formulation facilitates an optimal order convergence in the L2 norm as well as the energy norm. Several numerical examples are presented to show the performance of the method.
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics