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Volume 37, Issue 4
A Discontinuous Galerkin Method by Patch Reconstruction for Biharmonic Problem

Ruo Li, Pingbing Ming, Zhiyuan Sun, Fanyi Yang & Jerry Zhijian Yang

J. Comp. Math., 37 (2019), pp. 524-540.

Published online: 2019-02

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  • Abstract

We propose a new discontinuous Galerkin method based on the least-squares patch reconstruction for the biharmonic problem. We prove the optimal error estimate of the proposed method. The two-dimensional and three-dimensional numerical examples are presented to confirm the accuracy and efficiency of the method with several boundary conditions and several types of polygon meshes and polyhedral meshes.

  • AMS Subject Headings

49N45, 65N21

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

rli@math.pku.edu.cn (Ruo Li)

mpb@lsec.cc.ac.cn (Pingbing Ming)

zysun@math.pku.edu.cn (Zhiyuan Sun)

yangfanyi@pku.edu.cn (Fanyi Yang)

zjyang.math@whu.edu.cn (Jerry Zhijian Yang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-37-524, author = {Li , RuoMing , PingbingSun , ZhiyuanYang , Fanyi and Yang , Jerry Zhijian}, title = {A Discontinuous Galerkin Method by Patch Reconstruction for Biharmonic Problem}, journal = {Journal of Computational Mathematics}, year = {2019}, volume = {37}, number = {4}, pages = {524--540}, abstract = {

We propose a new discontinuous Galerkin method based on the least-squares patch reconstruction for the biharmonic problem. We prove the optimal error estimate of the proposed method. The two-dimensional and three-dimensional numerical examples are presented to confirm the accuracy and efficiency of the method with several boundary conditions and several types of polygon meshes and polyhedral meshes.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1807-m2017-0276}, url = {http://global-sci.org/intro/article_detail/jcm/13007.html} }
TY - JOUR T1 - A Discontinuous Galerkin Method by Patch Reconstruction for Biharmonic Problem AU - Li , Ruo AU - Ming , Pingbing AU - Sun , Zhiyuan AU - Yang , Fanyi AU - Yang , Jerry Zhijian JO - Journal of Computational Mathematics VL - 4 SP - 524 EP - 540 PY - 2019 DA - 2019/02 SN - 37 DO - http://doi.org/10.4208/jcm.1807-m2017-0276 UR - https://global-sci.org/intro/article_detail/jcm/13007.html KW - Least-squares problem, Reconstructed basis function, Discontinuous Galerkin method, Biharmonic problem. AB -

We propose a new discontinuous Galerkin method based on the least-squares patch reconstruction for the biharmonic problem. We prove the optimal error estimate of the proposed method. The two-dimensional and three-dimensional numerical examples are presented to confirm the accuracy and efficiency of the method with several boundary conditions and several types of polygon meshes and polyhedral meshes.

Ruo Li, Pingbing Ming, Zhiyuan Sun, Fanyi Yang & Jerry Zhijian Yang. (2019). A Discontinuous Galerkin Method by Patch Reconstruction for Biharmonic Problem. Journal of Computational Mathematics. 37 (4). 524-540. doi:10.4208/jcm.1807-m2017-0276
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