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Volume 15, Issue 6
Local Analysis of the Local Discontinuous Galerkin Method with the Generalized Alternating Numerical Flux for Two-Dimensional Singularly Perturbed Problem

Yao Cheng, Qiang Zhang & Haijin Wang

Int. J. Numer. Anal. Mod., 15 (2018), pp. 785-810.

Published online: 2018-08

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  • Abstract

In this paper, we analyze the local discontinuous Galerkin method with the generalized alternating numerical flux for two-dimensional singularly perturbed problem with outflow boundary layers. By virtue of the two-dimensional generalized Gauss-Radau projection and energy technique with suitable weight function, we obtain the double-optimal error estimate, namely, the convergence rate in L2-norm out of the outflow boundary layer is optimal, and the width of boundary layer is quasi-optimal, when piecewise tensor product polynomial space on quasi-uniform Cartesian meshes are used. Numerical experiments are given to verify the theoretical results.

  • Keywords

Local analysis, local discontinuous Galerkin method, generalized alternating numerical flux, error estimate, singularly perturbed problem.

  • AMS Subject Headings

65M12, 65M15, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ycheng@usts.edu.cn (Yao Cheng)

qzh@nju.edu.cn (Qiang Zhang)

hjwang@njupt.edu.cn (Haijin Wang)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-15-785, author = {Cheng , YaoZhang , Qiang and Wang , Haijin}, title = {Local Analysis of the Local Discontinuous Galerkin Method with the Generalized Alternating Numerical Flux for Two-Dimensional Singularly Perturbed Problem}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {15}, number = {6}, pages = {785--810}, abstract = {

In this paper, we analyze the local discontinuous Galerkin method with the generalized alternating numerical flux for two-dimensional singularly perturbed problem with outflow boundary layers. By virtue of the two-dimensional generalized Gauss-Radau projection and energy technique with suitable weight function, we obtain the double-optimal error estimate, namely, the convergence rate in L2-norm out of the outflow boundary layer is optimal, and the width of boundary layer is quasi-optimal, when piecewise tensor product polynomial space on quasi-uniform Cartesian meshes are used. Numerical experiments are given to verify the theoretical results.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12609.html} }
TY - JOUR T1 - Local Analysis of the Local Discontinuous Galerkin Method with the Generalized Alternating Numerical Flux for Two-Dimensional Singularly Perturbed Problem AU - Cheng , Yao AU - Zhang , Qiang AU - Wang , Haijin JO - International Journal of Numerical Analysis and Modeling VL - 6 SP - 785 EP - 810 PY - 2018 DA - 2018/08 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/12609.html KW - Local analysis, local discontinuous Galerkin method, generalized alternating numerical flux, error estimate, singularly perturbed problem. AB -

In this paper, we analyze the local discontinuous Galerkin method with the generalized alternating numerical flux for two-dimensional singularly perturbed problem with outflow boundary layers. By virtue of the two-dimensional generalized Gauss-Radau projection and energy technique with suitable weight function, we obtain the double-optimal error estimate, namely, the convergence rate in L2-norm out of the outflow boundary layer is optimal, and the width of boundary layer is quasi-optimal, when piecewise tensor product polynomial space on quasi-uniform Cartesian meshes are used. Numerical experiments are given to verify the theoretical results.

Cheng , YaoZhang , Qiang and Wang , Haijin. (2018). Local Analysis of the Local Discontinuous Galerkin Method with the Generalized Alternating Numerical Flux for Two-Dimensional Singularly Perturbed Problem. International Journal of Numerical Analysis and Modeling. 15 (6). 785-810. doi:
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