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

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 $L$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.

65N12 65N30.

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

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@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 $L$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 KW - staggered discontinuous Galerkin method KW - 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 $L$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.

Siu Wun Cheung & Eric T. Chung. (2020). 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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