A hybrid discontinuous Galerkin method for advection-diffusion-reaction problems

Dong Wook Shin; Youngmok Jeon; Eun Jae Park

doi:10.1016/j.apnum.2014.11.003

A hybrid discontinuous Galerkin method for advection-diffusion-reaction problems

Dong Wook Shin, Youngmok Jeon, Eun Jae Park

Department of Computational Science and Engineering

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	292-303
Number of pages	12
Journal	Applied Numerical Mathematics
Volume	95
DOIs	https://doi.org/10.1016/j.apnum.2014.11.003
Publication status	Published - 2015 May 26

Bibliographical note

Publisher Copyright:
© 2014 IMACS. Published by Elsevier B.V. Allrightsreserved.

All Science Journal Classification (ASJC) codes

Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1016/j.apnum.2014.11.003

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abstract = "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.",

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AB - 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.

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A hybrid discontinuous Galerkin method for advection-diffusion-reaction problems

Abstract

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