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
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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