Numerical Analysis of Least-Squares Group Finite Element Method for Coupled Burgers' Problem
In this paper, a least squares group finite element method for solving coupled Burgers' problem in 2-D is presented. A fully discrete formulation of least squares finite element method is analyzed, the backward-Euler scheme for the time variable is considered, the discretization with respect...
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| Format: | Article |
| Language: | Arabic |
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College of Science for Women, University of Baghdad
2021-12-01
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| Series: | Baghdad Science Journal |
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| Online Access: | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/3782 |
| _version_ | 1818893203332399104 |
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| author | Najat Jalil Noon |
| author_facet | Najat Jalil Noon |
| author_sort | Najat Jalil Noon |
| collection | DOAJ |
| description | In this paper, a least squares group finite element method for solving coupled Burgers' problem in 2-D is presented. A fully discrete formulation of least squares finite element method is analyzed, the backward-Euler scheme for the time variable is considered, the discretization with respect to space variable is applied as biquadratic quadrangular elements with nine nodes for each element. The continuity, ellipticity, stability condition and error estimate of least squares group finite element method are proved. The theoretical results show that the error estimate of this method is . The numerical results are compared with the exact solution and other available literature when the convection-dominated case to illustrate the efficiency of the proposed method that are solved through implementation in MATLAB R2018a. |
| first_indexed | 2024-12-19T18:08:52Z |
| format | Article |
| id | doaj.art-c94c53ed3dc24deab14d05565b294bd4 |
| institution | Directory Open Access Journal |
| issn | 2078-8665 2411-7986 |
| language | Arabic |
| last_indexed | 2024-12-19T18:08:52Z |
| publishDate | 2021-12-01 |
| publisher | College of Science for Women, University of Baghdad |
| record_format | Article |
| series | Baghdad Science Journal |
| spelling | doaj.art-c94c53ed3dc24deab14d05565b294bd42022-12-21T20:11:23ZaraCollege of Science for Women, University of BaghdadBaghdad Science Journal2078-86652411-79862021-12-01184(Suppl.)10.21123/bsj.2021.18.4(Suppl.).1521Numerical Analysis of Least-Squares Group Finite Element Method for Coupled Burgers' ProblemNajat Jalil Noon0Department of Mathematics, College of Education for Pure Science, University of BasrahIn this paper, a least squares group finite element method for solving coupled Burgers' problem in 2-D is presented. A fully discrete formulation of least squares finite element method is analyzed, the backward-Euler scheme for the time variable is considered, the discretization with respect to space variable is applied as biquadratic quadrangular elements with nine nodes for each element. The continuity, ellipticity, stability condition and error estimate of least squares group finite element method are proved. The theoretical results show that the error estimate of this method is . The numerical results are compared with the exact solution and other available literature when the convection-dominated case to illustrate the efficiency of the proposed method that are solved through implementation in MATLAB R2018a.https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/3782Burgers' problem, Group finite element method, Least square |
| spellingShingle | Najat Jalil Noon Numerical Analysis of Least-Squares Group Finite Element Method for Coupled Burgers' Problem Baghdad Science Journal Burgers' problem, Group finite element method, Least square |
| title | Numerical Analysis of Least-Squares Group Finite Element Method for Coupled Burgers' Problem |
| title_full | Numerical Analysis of Least-Squares Group Finite Element Method for Coupled Burgers' Problem |
| title_fullStr | Numerical Analysis of Least-Squares Group Finite Element Method for Coupled Burgers' Problem |
| title_full_unstemmed | Numerical Analysis of Least-Squares Group Finite Element Method for Coupled Burgers' Problem |
| title_short | Numerical Analysis of Least-Squares Group Finite Element Method for Coupled Burgers' Problem |
| title_sort | numerical analysis of least squares group finite element method for coupled burgers problem |
| topic | Burgers' problem, Group finite element method, Least square |
| url | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/3782 |
| work_keys_str_mv | AT najatjalilnoon numericalanalysisofleastsquaresgroupfiniteelementmethodforcoupledburgersproblem |