Optimal error estimates of the local discontinuous Galerkin methods based on generalized fluxes for 1D linear fifth order partial differential equations
Abstract In this paper, we study the error estimates of local discontinuous Galerkin methods based on the generalized numerical fluxes for the one-dimensional linear fifth order partial differential equations. We use a newly developed global Gauss–Radau projection to obtain the linear type of optima...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-08-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-022-02843-8 |
| _version_ | 1811215399631454208 |
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| author | Hui Bi Yixin Chen |
| author_facet | Hui Bi Yixin Chen |
| author_sort | Hui Bi |
| collection | DOAJ |
| description | Abstract In this paper, we study the error estimates of local discontinuous Galerkin methods based on the generalized numerical fluxes for the one-dimensional linear fifth order partial differential equations. We use a newly developed global Gauss–Radau projection to obtain the linear type of optimal error estimates. The numerical experiments show that the scheme coupled with the third order implicit Runge–Kutta method can achieve the optimal ( k + 1 ) $(k+1)$ th order of accuracy. |
| first_indexed | 2024-04-12T06:22:01Z |
| format | Article |
| id | doaj.art-ea537efc16f34e3b907bec6ac86ee3ce |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-12T06:22:01Z |
| publishDate | 2022-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-ea537efc16f34e3b907bec6ac86ee3ce2022-12-22T03:44:17ZengSpringerOpenJournal of Inequalities and Applications1029-242X2022-08-012022111910.1186/s13660-022-02843-8Optimal error estimates of the local discontinuous Galerkin methods based on generalized fluxes for 1D linear fifth order partial differential equationsHui Bi0Yixin Chen1Department of Mathematics, Harbin University of Science and TechnologyDepartment of Mathematics, Harbin University of Science and TechnologyAbstract In this paper, we study the error estimates of local discontinuous Galerkin methods based on the generalized numerical fluxes for the one-dimensional linear fifth order partial differential equations. We use a newly developed global Gauss–Radau projection to obtain the linear type of optimal error estimates. The numerical experiments show that the scheme coupled with the third order implicit Runge–Kutta method can achieve the optimal ( k + 1 ) $(k+1)$ th order of accuracy.https://doi.org/10.1186/s13660-022-02843-8Local discontinuous Galerkin methodsFifth order partial differential equationsGlobal Gauss–Radau projectionError estimates |
| spellingShingle | Hui Bi Yixin Chen Optimal error estimates of the local discontinuous Galerkin methods based on generalized fluxes for 1D linear fifth order partial differential equations Journal of Inequalities and Applications Local discontinuous Galerkin methods Fifth order partial differential equations Global Gauss–Radau projection Error estimates |
| title | Optimal error estimates of the local discontinuous Galerkin methods based on generalized fluxes for 1D linear fifth order partial differential equations |
| title_full | Optimal error estimates of the local discontinuous Galerkin methods based on generalized fluxes for 1D linear fifth order partial differential equations |
| title_fullStr | Optimal error estimates of the local discontinuous Galerkin methods based on generalized fluxes for 1D linear fifth order partial differential equations |
| title_full_unstemmed | Optimal error estimates of the local discontinuous Galerkin methods based on generalized fluxes for 1D linear fifth order partial differential equations |
| title_short | Optimal error estimates of the local discontinuous Galerkin methods based on generalized fluxes for 1D linear fifth order partial differential equations |
| title_sort | optimal error estimates of the local discontinuous galerkin methods based on generalized fluxes for 1d linear fifth order partial differential equations |
| topic | Local discontinuous Galerkin methods Fifth order partial differential equations Global Gauss–Radau projection Error estimates |
| url | https://doi.org/10.1186/s13660-022-02843-8 |
| work_keys_str_mv | AT huibi optimalerrorestimatesofthelocaldiscontinuousgalerkinmethodsbasedongeneralizedfluxesfor1dlinearfifthorderpartialdifferentialequations AT yixinchen optimalerrorestimatesofthelocaldiscontinuousgalerkinmethodsbasedongeneralizedfluxesfor1dlinearfifthorderpartialdifferentialequations |