A Scharfetter-Gummerl stabilization scheme for HDG approximations of convection-diffusion problems

Abstract: We present a Scharfetter-Gummel (SG) stabilization scheme for high-order Hybrid Discontinuous Galerkin (HDG) approximations of convection-diffusion problems. The scheme is based on a careful choice of the stabilization parameters used to define the numerical flux in the HDG method. We show that, in one dimension, the SG-HDG scheme is equivalent to the Finite Volume method stabilized with the Scharfetter--Gummel on the dual grid, for all orders of HDG schemes.