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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.

Yang , WeiCao , LulingHuang , Yunqing and Cui , Jintao. (2018). 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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