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arXiv · 2211.01648

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

Stefano Piani·Luca Heltai·Wenyu Lei
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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.

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Stefano Piani, Luca Heltai, Wenyu Lei. 2022-11-03. A Scharfetter-Gummerl stabilization scheme for HDG approximations of convection-diffusion problems. https://arxiv.org/abs/2211.01648

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