Stability and convergence of a local discontinuous Galerkin finite element method for the general Lax equation
In this paper we develop and analyze the local discontinuous Galerkin (LDG) finite element method for solving the general Lax equation. The local discontinuous Galerkin method has the flexibility for arbitrary h and p adaptivity, and allows for hanging nodes. By choosing the numerical fluxes careful...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-09-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2018-0091 |
| _version_ | 1818720382457217024 |
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| author | Wei Leilei Mu Yundong |
| author_facet | Wei Leilei Mu Yundong |
| author_sort | Wei Leilei |
| collection | DOAJ |
| description | In this paper we develop and analyze the local discontinuous Galerkin (LDG) finite element method for solving the general Lax equation. The local discontinuous Galerkin method has the flexibility for arbitrary h and p adaptivity, and allows for hanging nodes. By choosing the numerical fluxes carefully we prove stability and give an error estimate. Finally some numerical examples are computed to show the convergence order and excellent numerical performance of proposed method. |
| first_indexed | 2024-12-17T20:21:57Z |
| format | Article |
| id | doaj.art-0ba0f0bbc5bc48e6a6ecb84c3abe13d4 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-17T20:21:57Z |
| publishDate | 2018-09-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-0ba0f0bbc5bc48e6a6ecb84c3abe13d42022-12-21T21:33:55ZengDe GruyterOpen Mathematics2391-54552018-09-011611091110310.1515/math-2018-0091math-2018-0091Stability and convergence of a local discontinuous Galerkin finite element method for the general Lax equationWei Leilei0Mu Yundong1College of Science, Henan University of Technology, Zhengzhou, Henan 450001, ChinaCollege of Science, Henan University of Technology, Zhengzhou, Henan 450001, ChinaIn this paper we develop and analyze the local discontinuous Galerkin (LDG) finite element method for solving the general Lax equation. The local discontinuous Galerkin method has the flexibility for arbitrary h and p adaptivity, and allows for hanging nodes. By choosing the numerical fluxes carefully we prove stability and give an error estimate. Finally some numerical examples are computed to show the convergence order and excellent numerical performance of proposed method.https://doi.org/10.1515/math-2018-0091lax equationlocal discontinuous galerkin methodstability analysiserror estimates35s1065m12 |
| spellingShingle | Wei Leilei Mu Yundong Stability and convergence of a local discontinuous Galerkin finite element method for the general Lax equation Open Mathematics lax equation local discontinuous galerkin method stability analysis error estimates 35s10 65m12 |
| title | Stability and convergence of a local discontinuous Galerkin finite element method for the general Lax equation |
| title_full | Stability and convergence of a local discontinuous Galerkin finite element method for the general Lax equation |
| title_fullStr | Stability and convergence of a local discontinuous Galerkin finite element method for the general Lax equation |
| title_full_unstemmed | Stability and convergence of a local discontinuous Galerkin finite element method for the general Lax equation |
| title_short | Stability and convergence of a local discontinuous Galerkin finite element method for the general Lax equation |
| title_sort | stability and convergence of a local discontinuous galerkin finite element method for the general lax equation |
| topic | lax equation local discontinuous galerkin method stability analysis error estimates 35s10 65m12 |
| url | https://doi.org/10.1515/math-2018-0091 |
| work_keys_str_mv | AT weileilei stabilityandconvergenceofalocaldiscontinuousgalerkinfiniteelementmethodforthegenerallaxequation AT muyundong stabilityandconvergenceofalocaldiscontinuousgalerkinfiniteelementmethodforthegenerallaxequation |