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Volume 16, Issue 2
A New $a$ $Posteriori$ Error Estimate for the Interior Penalty Discontinuous Galerkin Method

Wei Yang, Luling Cao, Yunqing Huang & Jintao Cui

Int. J. Numer. Anal. Mod., 16 (2019), pp. 210-224.

Published online: 2018-10

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  • Abstract

In this paper, we develop the adaptive interior penalty discontinuous Galerkin method based on a new $a$ $posteriori$ error estimate for the second-order elliptic boundary-value problems. The new $a$ $posteriori$ error estimate is motivated from the smoothing iteration of the $m$-time Gauss-Seidel iterative method, and it is used to construct the adaptive finite element method. The efficiency and robustness of the proposed adaptive method is demonstrated by extensive numerical experiments.

  • Keywords

Interior penalty discontinuous Galerkin method, a posteriori error estimate, adaptive finite element methods, Gauss-Seidel iterative method.

  • AMS Subject Headings

65N15, 65N30, 35J20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yangwei@xtu.edu.cn (Wei Yang)

lulingcao@163.com (Luling Cao)

huangyq@xtu.edu.cn (Yunqing Huang)

jintao.cui@polyu.edu.hk (Jintao Cui)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-16-210, author = {Yang , WeiCao , LulingHuang , Yunqing and Cui , Jintao}, title = {A New $a$ $Posteriori$ Error Estimate for the Interior Penalty Discontinuous Galerkin Method}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {16}, number = {2}, pages = {210--224}, abstract = {

In this paper, we develop the adaptive interior penalty discontinuous Galerkin method based on a new $a$ $posteriori$ error estimate for the second-order elliptic boundary-value problems. The new $a$ $posteriori$ error estimate is motivated from the smoothing iteration of the $m$-time Gauss-Seidel iterative method, and it is used to construct the adaptive finite element method. The efficiency and robustness of the proposed adaptive method is demonstrated by extensive numerical experiments.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12800.html} }
TY - JOUR T1 - A New $a$ $Posteriori$ Error Estimate for the Interior Penalty Discontinuous Galerkin Method AU - Yang , Wei AU - Cao , Luling AU - Huang , Yunqing AU - Cui , Jintao JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 210 EP - 224 PY - 2018 DA - 2018/10 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/12800.html KW - Interior penalty discontinuous Galerkin method, a posteriori error estimate, adaptive finite element methods, Gauss-Seidel iterative method. AB -

In this paper, we develop the adaptive interior penalty discontinuous Galerkin method based on a new $a$ $posteriori$ error estimate for the second-order elliptic boundary-value problems. The new $a$ $posteriori$ error estimate is motivated from the smoothing iteration of the $m$-time Gauss-Seidel iterative method, and it is used to construct the adaptive finite element method. The efficiency and robustness of the proposed adaptive method is demonstrated by extensive numerical experiments.

Wei Yang, Luling Cao, Yunqing Huang & Jintao Cui. (2020). A New $a$ $Posteriori$ Error Estimate for the Interior Penalty Discontinuous Galerkin Method. International Journal of Numerical Analysis and Modeling. 16 (2). 210-224. doi:
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