### Electronic Research Archive

2020, Issue 4: 1487-1501. doi: 10.3934/era.2020078
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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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沈阳化工大学材料科学与工程学院 沈阳 110142

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