Two-Grid Method for Burgers’ Equation by a New Mixed Finite Element Scheme
In this article, we present two-grid stable mixed finite element method for the 2D Burgers’ equation approximated by the -P1 pair which satisfies the inf–sup condition. This method consists in dealing with the nonlinear system on a coarse mesh with width H and the linear system on a fine mesh with w...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2014-02-01
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| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/3256 |
| _version_ | 1811190392074272768 |
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| author | Xiaohui Hu Pengzhan Huang Xinlong Feng |
| author_facet | Xiaohui Hu Pengzhan Huang Xinlong Feng |
| author_sort | Xiaohui Hu |
| collection | DOAJ |
| description | In this article, we present two-grid stable mixed finite element method for the 2D Burgers’ equation approximated by the -P1 pair which satisfies the inf–sup condition. This method consists in dealing with the nonlinear system on a coarse mesh with width H and the linear system on a fine mesh with width h << H by using Crank–Nicolson time-discretization scheme. Our results show that if we choose H2 = h this method can achieve asymptotically optimal approximation. Error estimates are derived in detail. Finally, numerical experiments show the efficiency of our proposed method and justify the theoretical results. |
| first_indexed | 2024-04-11T14:49:27Z |
| format | Article |
| id | doaj.art-5bac6c20656a47daaeb945c19d9e3f87 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-04-11T14:49:27Z |
| publishDate | 2014-02-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-5bac6c20656a47daaeb945c19d9e3f872022-12-22T04:17:32ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102014-02-0119110.3846/13926292.2014.892902Two-Grid Method for Burgers’ Equation by a New Mixed Finite Element SchemeXiaohui Hu0Pengzhan Huang1Xinlong Feng2Xinjiang University 830046 Urumqi, ChinaXinjiang University 830046 Urumqi, ChinaXinjiang University 830046 Urumqi, ChinaIn this article, we present two-grid stable mixed finite element method for the 2D Burgers’ equation approximated by the -P1 pair which satisfies the inf–sup condition. This method consists in dealing with the nonlinear system on a coarse mesh with width H and the linear system on a fine mesh with width h << H by using Crank–Nicolson time-discretization scheme. Our results show that if we choose H2 = h this method can achieve asymptotically optimal approximation. Error estimates are derived in detail. Finally, numerical experiments show the efficiency of our proposed method and justify the theoretical results.https://journals.vgtu.lt/index.php/MMA/article/view/3256Burgers’ equationtwo-grid methodstable conforming finite elementCrank-Nicolson schemeinf-sup condition |
| spellingShingle | Xiaohui Hu Pengzhan Huang Xinlong Feng Two-Grid Method for Burgers’ Equation by a New Mixed Finite Element Scheme Mathematical Modelling and Analysis Burgers’ equation two-grid method stable conforming finite element Crank-Nicolson scheme inf-sup condition |
| title | Two-Grid Method for Burgers’ Equation by a New Mixed Finite Element Scheme |
| title_full | Two-Grid Method for Burgers’ Equation by a New Mixed Finite Element Scheme |
| title_fullStr | Two-Grid Method for Burgers’ Equation by a New Mixed Finite Element Scheme |
| title_full_unstemmed | Two-Grid Method for Burgers’ Equation by a New Mixed Finite Element Scheme |
| title_short | Two-Grid Method for Burgers’ Equation by a New Mixed Finite Element Scheme |
| title_sort | two grid method for burgers equation by a new mixed finite element scheme |
| topic | Burgers’ equation two-grid method stable conforming finite element Crank-Nicolson scheme inf-sup condition |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/3256 |
| work_keys_str_mv | AT xiaohuihu twogridmethodforburgersequationbyanewmixedfiniteelementscheme AT pengzhanhuang twogridmethodforburgersequationbyanewmixedfiniteelementscheme AT xinlongfeng twogridmethodforburgersequationbyanewmixedfiniteelementscheme |