$hp$-optimal convergence of the original DG method for linear hyperbolic problems on special simplicial meshes
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914862155694080 |
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| author | Dong, Zhaonan Mascotto, Lorenzo |
| author_facet | Dong, Zhaonan Mascotto, Lorenzo |
| contents | We prove hp-optimal error estimates for the original DG method when approximating solutions to first-order hyperbolic problems with constant convection fields in the L2 and DG norms. The main theoretical tools used in the analysis are novel hp-optimal approximation properties of the special projector introduced in [Cockburn, Dong, Guzman, SINUM, 2008]. We assess the theoretical findings on some test cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_13564 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $hp$-optimal convergence of the original DG method for linear hyperbolic problems on special simplicial meshes Dong, Zhaonan Mascotto, Lorenzo Numerical Analysis 65N12, 65N30, 65N50 We prove hp-optimal error estimates for the original DG method when approximating solutions to first-order hyperbolic problems with constant convection fields in the L2 and DG norms. The main theoretical tools used in the analysis are novel hp-optimal approximation properties of the special projector introduced in [Cockburn, Dong, Guzman, SINUM, 2008]. We assess the theoretical findings on some test cases. |
| title | $hp$-optimal convergence of the original DG method for linear hyperbolic problems on special simplicial meshes |
| topic | Numerical Analysis 65N12, 65N30, 65N50 |
| url | https://arxiv.org/abs/2310.13564 |