A Priori Error Estimates for Mixed Finite Element Schemes for the Wave Equation
A family of implicit-in-time mixed finite element schemes is presented for the numerical approximation of the acoustic wave equation. The mixed space discretization is based on the displacement form of the wave equation and the time-stepping method employs a three-level one-parameter scheme. A rigor...
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| Format: | Article |
| Language: | English |
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Sultan Qaboos University
2015-12-01
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| Series: | Sultan Qaboos University Journal for Science |
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| Online Access: | https://journals.squ.edu.om/index.php/squjs/article/view/442 |
| _version_ | 1811240239439544320 |
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| author | Samir Karaa |
| author_facet | Samir Karaa |
| author_sort | Samir Karaa |
| collection | DOAJ |
| description | A family of implicit-in-time mixed finite element schemes is presented for the numerical approximation of the acoustic wave equation. The mixed space discretization is based on the displacement form of the wave equation and the time-stepping method employs a three-level one-parameter scheme. A rigorous stability analysis is presented based on energy estimation and sharp stability results are obtained. A convergence analysis is carried out and optimal a priorierror estimates for both displacement and pressure are derived. |
| first_indexed | 2024-04-12T13:15:33Z |
| format | Article |
| id | doaj.art-a7e9fdf313ed488a9d896e2629f920ff |
| institution | Directory Open Access Journal |
| issn | 1027-524X 2414-536X |
| language | English |
| last_indexed | 2024-04-12T13:15:33Z |
| publishDate | 2015-12-01 |
| publisher | Sultan Qaboos University |
| record_format | Article |
| series | Sultan Qaboos University Journal for Science |
| spelling | doaj.art-a7e9fdf313ed488a9d896e2629f920ff2022-12-22T03:31:42ZengSultan Qaboos UniversitySultan Qaboos University Journal for Science1027-524X2414-536X2015-12-01202314110.24200/squjs.vol20iss2pp31-41437A Priori Error Estimates for Mixed Finite Element Schemes for the Wave EquationSamir Karaa0Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.O. Box: 36, Al-Khod 123, Muscat, Sultanate of Oman.A family of implicit-in-time mixed finite element schemes is presented for the numerical approximation of the acoustic wave equation. The mixed space discretization is based on the displacement form of the wave equation and the time-stepping method employs a three-level one-parameter scheme. A rigorous stability analysis is presented based on energy estimation and sharp stability results are obtained. A convergence analysis is carried out and optimal a priorierror estimates for both displacement and pressure are derived.https://journals.squ.edu.om/index.php/squjs/article/view/442Energy techniqueError estimationMixed finite elementsWave equation. |
| spellingShingle | Samir Karaa A Priori Error Estimates for Mixed Finite Element Schemes for the Wave Equation Sultan Qaboos University Journal for Science Energy technique Error estimation Mixed finite elements Wave equation. |
| title | A Priori Error Estimates for Mixed Finite Element Schemes for the Wave Equation |
| title_full | A Priori Error Estimates for Mixed Finite Element Schemes for the Wave Equation |
| title_fullStr | A Priori Error Estimates for Mixed Finite Element Schemes for the Wave Equation |
| title_full_unstemmed | A Priori Error Estimates for Mixed Finite Element Schemes for the Wave Equation |
| title_short | A Priori Error Estimates for Mixed Finite Element Schemes for the Wave Equation |
| title_sort | priori error estimates for mixed finite element schemes for the wave equation |
| topic | Energy technique Error estimation Mixed finite elements Wave equation. |
| url | https://journals.squ.edu.om/index.php/squjs/article/view/442 |
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