A Discontinuous Galerkin Method by Patch Reconstruction for Biharmonic Problem

Authors

  • Ruo Li HEDPS & CAPT, LMAM & School of Mathematical Sciences, Peking University, Beijing, China
  • Pingbing Ming LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of Sciences, Beijing, 100190, China
  • Zhiyuan Sun School of Mathematical Sciences, Peking University, Beijing 100871, China
  • Fanyi Yang School of Mathematical Sciences, Peking University, Beijing 100871, China
  • Jerry Zhijian Yang School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

DOI:

https://doi.org/10.4208/jcm.1807-m2017-0276

Keywords:

Least-squares problem, Reconstructed basis function, Discontinuous Galerkin method, Biharmonic problem.

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.

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Published

2019-04-29

Issue

Vol. 37 No. 4 (2019)

Section

Articles