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A numerical study of superconvergence of the discontinuous Galerkin method by patch reconstruction

  • Received: 01 March 2020 Revised: 01 June 2020 Published: 31 July 2020
  • Primary: 49N45; Secondary: 65N21

  • We numerically investigate the superconvergence property of the discontinuous Galerkin method by patch reconstruction. The convergence rate $ 2m+1 $ can be observed at the grid points and barycenters in one dimensional case with uniform partitions. The convergence rate $ m + 2 $ is achieved at the center of the element faces in two and three dimensions. The meshes are uniformly partitioned into triangles/tetrahedrons or squares/hexahedrons. We also demonstrate the details of the implementation of the proposed method. The numerical results for all three dimensional cases are presented to illustrate the propositions.

    Citation: Zexuan Liu, Zhiyuan Sun, Jerry Zhijian Yang. A numerical study of superconvergence of the discontinuous Galerkin method by patch reconstruction[J]. Electronic Research Archive, 2020, 28(4): 1487-1501. doi: 10.3934/era.2020078

    Related Papers:

  • We numerically investigate the superconvergence property of the discontinuous Galerkin method by patch reconstruction. The convergence rate $ 2m+1 $ can be observed at the grid points and barycenters in one dimensional case with uniform partitions. The convergence rate $ m + 2 $ is achieved at the center of the element faces in two and three dimensions. The meshes are uniformly partitioned into triangles/tetrahedrons or squares/hexahedrons. We also demonstrate the details of the implementation of the proposed method. The numerical results for all three dimensional cases are presented to illustrate the propositions.



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