An analysis of HDG methods for convection-dominated diffusion problems

Fu, Guosheng; Qiu, Weifeng; Zhang, Wujun

doi:10.1051/m2an/2014032

Fu, Guosheng ¹ ; Qiu, Weifeng ² ; Zhang, Wujun ³

¹ School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA.
² Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, P.R. China.
³ Department of Mathematics, University of Maryland, College Park, MD 20742-4015, USA.

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 1, pp. 225-256.

Résumé

We present the first a priori error analysis of the $h$ -version of the hybridizable discontinuous Galkerin (HDG) methods applied to convection-dominated diffusion problems. We show that, when using polynomials of degree no greater than $k$ , the $L^{2}$ -error of the scalar variable converges with order $k + 1 / 2$ on general conforming quasi-uniform simplicial meshes, just as for conventional DG methods. We also show that the method achieves the optimal $L^{2}$ -convergence order of $k + 1$ on special meshes. Moreover, we discuss a new way of implementing the HDG methods for which the spectral condition number of the global matrix is independent of the diffusion coefficient. Numerical experiments are presented which verify our theoretical results.

Reçu le : 2013-10-03

MR Zbl | 1 citation dans Numdam

DOI : 10.1051/m2an/2014032

Classification : 65N30
Mots-clés : HDG, convection-dominated diffusion

Affiliations des auteurs :

Fu, Guosheng ¹ ; Qiu, Weifeng ² ; Zhang, Wujun ³

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     title = {An analysis of {HDG} methods for convection-dominated diffusion problems},
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Fu, Guosheng; Qiu, Weifeng; Zhang, Wujun. An analysis of HDG methods for convection-dominated diffusion problems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 1, pp. 225-256. doi : 10.1051/m2an/2014032. https://www.numdam.org/articles/10.1051/m2an/2014032/

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