The a posteriori error estimates of the Ciarlet-Raviart mixed finite element method for the biharmonic eigenvalue problem
The biharmonic equation/eigenvalue problem is one of the fundamental model problems in mathematics and physics and has wide applications. In this paper, for the biharmonic eigenvalue problem, based on the work of Gudi [<i>Numer. Methods Partial Differ. Equ.</i>, <b>27</b> (20...
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AIMS Press
2024-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://aimspress.com/article/doi/10.3934/math.2024163?viewType=HTML |
| _version_ | 1797348714188111872 |
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| author | Jinhua Feng Shixi Wang Hai Bi Yidu Yang |
| author_facet | Jinhua Feng Shixi Wang Hai Bi Yidu Yang |
| author_sort | Jinhua Feng |
| collection | DOAJ |
| description | The biharmonic equation/eigenvalue problem is one of the fundamental model problems in mathematics and physics and has wide applications. In this paper, for the biharmonic eigenvalue problem, based on the work of Gudi [<i>Numer. Methods Partial Differ. Equ.</i>, <b>27</b> (2011), 315-328], we study the a posteriori error estimates of the approximate eigenpairs obtained by the Ciarlet-Raviart mixed finite element method. We prove the reliability and efficiency of the error estimator of the approximate eigenfunction and analyze the reliability of the error estimator of the approximate eigenvalues. We also implement the adaptive calculation and exhibit the numerical experiments which show that our method is efficient and can get an approximate solution with high accuracy. |
| first_indexed | 2024-03-08T12:09:57Z |
| format | Article |
| id | doaj.art-b872a63540b04705a09d891d40018b72 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-08T12:09:57Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-b872a63540b04705a09d891d40018b722024-01-23T01:34:17ZengAIMS PressAIMS Mathematics2473-69882024-01-01923332334810.3934/math.2024163The a posteriori error estimates of the Ciarlet-Raviart mixed finite element method for the biharmonic eigenvalue problemJinhua Feng0Shixi Wang1Hai Bi2Yidu Yang31. Qiushi College, Guizhou Normal University, Guiyang, Guizhou 550025, China 2. School of Mathematical Sciences, Guizhou Normal University, Guiyang, Guizhou 550025, China2. School of Mathematical Sciences, Guizhou Normal University, Guiyang, Guizhou 550025, China2. School of Mathematical Sciences, Guizhou Normal University, Guiyang, Guizhou 550025, China2. School of Mathematical Sciences, Guizhou Normal University, Guiyang, Guizhou 550025, ChinaThe biharmonic equation/eigenvalue problem is one of the fundamental model problems in mathematics and physics and has wide applications. In this paper, for the biharmonic eigenvalue problem, based on the work of Gudi [<i>Numer. Methods Partial Differ. Equ.</i>, <b>27</b> (2011), 315-328], we study the a posteriori error estimates of the approximate eigenpairs obtained by the Ciarlet-Raviart mixed finite element method. We prove the reliability and efficiency of the error estimator of the approximate eigenfunction and analyze the reliability of the error estimator of the approximate eigenvalues. We also implement the adaptive calculation and exhibit the numerical experiments which show that our method is efficient and can get an approximate solution with high accuracy.https://aimspress.com/article/doi/10.3934/math.2024163?viewType=HTMLthe biharmonic eigenvalueciarlet-raviart mixed methodconforming finite elementa posteriori error estimatoradaptive algorithm |
| spellingShingle | Jinhua Feng Shixi Wang Hai Bi Yidu Yang The a posteriori error estimates of the Ciarlet-Raviart mixed finite element method for the biharmonic eigenvalue problem AIMS Mathematics the biharmonic eigenvalue ciarlet-raviart mixed method conforming finite element a posteriori error estimator adaptive algorithm |
| title | The a posteriori error estimates of the Ciarlet-Raviart mixed finite element method for the biharmonic eigenvalue problem |
| title_full | The a posteriori error estimates of the Ciarlet-Raviart mixed finite element method for the biharmonic eigenvalue problem |
| title_fullStr | The a posteriori error estimates of the Ciarlet-Raviart mixed finite element method for the biharmonic eigenvalue problem |
| title_full_unstemmed | The a posteriori error estimates of the Ciarlet-Raviart mixed finite element method for the biharmonic eigenvalue problem |
| title_short | The a posteriori error estimates of the Ciarlet-Raviart mixed finite element method for the biharmonic eigenvalue problem |
| title_sort | a posteriori error estimates of the ciarlet raviart mixed finite element method for the biharmonic eigenvalue problem |
| topic | the biharmonic eigenvalue ciarlet-raviart mixed method conforming finite element a posteriori error estimator adaptive algorithm |
| url | https://aimspress.com/article/doi/10.3934/math.2024163?viewType=HTML |
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