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Volume 16, Issue 2
An Embedded SDG Method for the Convection-Diffusion Equation

Siu Wun Cheung & Eric T. Chung

Int. J. Numer. Anal. Mod., 16 (2019), pp. 255-275.

Published online: 2018-10

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  • Abstract

In this paper, we present an embedded staggered discontinuous Galerkin method for the convection-diffusion equation. The new method combines the advantages of staggered discontinuous Galerkin (SDG) and embedded discontinuous Galerkin (EDG) method, and results in many good properties, namely local and global conservations, free of carefully designed stabilization terms or flux conditions and high computational efficiency. In applying the new method to convection-dominated problems, the method provides optimal convergence in potential and suboptimal convergence in flux, which is comparable to other existing DG methods, and achieves $L$2 stability by making use of a skew-symmetric discretization of the convection term, irrespective of diffusivity. We will present numerical results to show the performance of the method.

  • Keywords

Embedded method, staggered discontinuous Galerkin method, convection-diffusion equation.

  • AMS Subject Headings

65N12, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

tschung@math.cuhk.edu.hk (Eric T. Chung)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-16-255, author = {Cheung , Siu Wun and Chung , Eric T.}, title = {An Embedded SDG Method for the Convection-Diffusion Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {16}, number = {2}, pages = {255--275}, abstract = {

In this paper, we present an embedded staggered discontinuous Galerkin method for the convection-diffusion equation. The new method combines the advantages of staggered discontinuous Galerkin (SDG) and embedded discontinuous Galerkin (EDG) method, and results in many good properties, namely local and global conservations, free of carefully designed stabilization terms or flux conditions and high computational efficiency. In applying the new method to convection-dominated problems, the method provides optimal convergence in potential and suboptimal convergence in flux, which is comparable to other existing DG methods, and achieves $L$2 stability by making use of a skew-symmetric discretization of the convection term, irrespective of diffusivity. We will present numerical results to show the performance of the method.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12803.html} }
TY - JOUR T1 - An Embedded SDG Method for the Convection-Diffusion Equation AU - Cheung , Siu Wun AU - Chung , Eric T. JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 255 EP - 275 PY - 2018 DA - 2018/10 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/12803.html KW - Embedded method, staggered discontinuous Galerkin method, convection-diffusion equation. AB -

In this paper, we present an embedded staggered discontinuous Galerkin method for the convection-diffusion equation. The new method combines the advantages of staggered discontinuous Galerkin (SDG) and embedded discontinuous Galerkin (EDG) method, and results in many good properties, namely local and global conservations, free of carefully designed stabilization terms or flux conditions and high computational efficiency. In applying the new method to convection-dominated problems, the method provides optimal convergence in potential and suboptimal convergence in flux, which is comparable to other existing DG methods, and achieves $L$2 stability by making use of a skew-symmetric discretization of the convection term, irrespective of diffusivity. We will present numerical results to show the performance of the method.

Cheung , Siu Wun and Chung , Eric T.. (2018). An Embedded SDG Method for the Convection-Diffusion Equation. International Journal of Numerical Analysis and Modeling. 16 (2). 255-275. doi:
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