Stability Analysis of the Explicit Ｒunge-Kutta Local Discontinuous Galerkin Method
To analyze the stability of the local discontinuous Garlerkin method for heat equation，where the time discretization is the explicit TVD Ｒunge-Kutta method. For the sufficiently smooth solution case，when the finite element space is the k-th order piecewise polynomial space on the regular meshes，we...
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Harbin University of Science and Technology Publications
2017-12-01
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| Series: | Journal of Harbin University of Science and Technology |
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| Online Access: | https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=1463 |
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| _version_ | 1849222494194499584 |
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| author | BI Hui QIAN Chen-geng |
| author_facet | BI Hui QIAN Chen-geng |
| author_sort | BI Hui |
| collection | DOAJ |
| description | To analyze the stability of the local discontinuous Garlerkin method for heat equation，where the
time discretization is the explicit TVD Ｒunge-Kutta method. For the sufficiently smooth solution case，when the
finite element space is the k-th order piecewise polynomial space on the regular meshes，we use the finite element
analysis technique to proof the L2-norm stability for hear equation under the CFL condition τ≤λμ － 2h2，where τ，h
are the time step and the length of the element respectively，and μ，λ are constants independent of h，τ. |
| format | Article |
| id | doaj-art-0f650f0379ef4577a0cb2e797c3733ef |
| institution | Kabale University |
| issn | 1007-2683 |
| language | zho |
| publishDate | 2017-12-01 |
| publisher | Harbin University of Science and Technology Publications |
| record_format | Article |
| series | Journal of Harbin University of Science and Technology |
| spelling | doaj-art-0f650f0379ef4577a0cb2e797c3733ef2025-08-26T04:32:08ZzhoHarbin University of Science and Technology PublicationsJournal of Harbin University of Science and Technology1007-26832017-12-01220610911210.15938/j.jhust.2017.06.020Stability Analysis of the Explicit Ｒunge-Kutta Local Discontinuous Galerkin MethodBI Hui0QIAN Chen-geng1School of Applied Sciences，Harbin University of Science and Technology，Harbin 150080，ChinaSchool of Applied Sciences，Harbin University of Science and Technology，Harbin 150080，ChinaTo analyze the stability of the local discontinuous Garlerkin method for heat equation，where the time discretization is the explicit TVD Ｒunge-Kutta method. For the sufficiently smooth solution case，when the finite element space is the k-th order piecewise polynomial space on the regular meshes，we use the finite element analysis technique to proof the L2-norm stability for hear equation under the CFL condition τ≤λμ － 2h2，where τ，h are the time step and the length of the element respectively，and μ，λ are constants independent of h，τ.https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=1463ｒunge-kuttafinite elementstability analysispartial differential equationsl2-norm stability |
| spellingShingle | BI Hui QIAN Chen-geng Stability Analysis of the Explicit Ｒunge-Kutta Local Discontinuous Galerkin Method Journal of Harbin University of Science and Technology ｒunge-kutta finite element stability analysis partial differential equations l2-norm stability |
| title | Stability Analysis of the Explicit Ｒunge-Kutta Local Discontinuous Galerkin Method |
| title_full | Stability Analysis of the Explicit Ｒunge-Kutta Local Discontinuous Galerkin Method |
| title_fullStr | Stability Analysis of the Explicit Ｒunge-Kutta Local Discontinuous Galerkin Method |
| title_full_unstemmed | Stability Analysis of the Explicit Ｒunge-Kutta Local Discontinuous Galerkin Method |
| title_short | Stability Analysis of the Explicit Ｒunge-Kutta Local Discontinuous Galerkin Method |
| title_sort | stability analysis of the explicit runge kutta local discontinuous galerkin method |
| topic | ｒunge-kutta finite element stability analysis partial differential equations l2-norm stability |
| url | https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=1463 |
| work_keys_str_mv | AT bihui stabilityanalysisoftheexplicitrungekuttalocaldiscontinuousgalerkinmethod AT qianchengeng stabilityanalysisoftheexplicitrungekuttalocaldiscontinuousgalerkinmethod |