A numerical solution of parabolic quasi-variational inequality nonlinear using Newton-multigrid method
In this article, we apply three numerical methods to study the L�convergence of the Newton-multigrid method for parabolic quasi-variational inequalities with a nonlinear right-hand side. To discretize the problem, we utilize a finite element method for the operator and Euler scheme for the time. To...
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Ferdowsi University of Mashhad
2025
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| author | Bahi M. Beggas M. Nesba N. Imtiaz A. |
| author2 | 59562493500 |
| author_facet | 59562493500 Bahi M. Beggas M. Nesba N. Imtiaz A. |
| author_sort | Bahi M. |
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| collection | Institutional Repository |
| content_provider | Universiti Tenaga Nasional |
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| continent | Asia |
| country | Malaysia |
| description | In this article, we apply three numerical methods to study the L�convergence of the Newton-multigrid method for parabolic quasi-variational inequalities with a nonlinear right-hand side. To discretize the problem, we utilize a finite element method for the operator and Euler scheme for the time. To obtain the system discretization of the problem, we reformulate the parabolic quasi-variational inequality as a Hamilton?Jacobi?Bellman equation. For linearizing the problem on the coarse grid, we employ Newton?s method as an external interior iteration of the Jacobian system. On the smooth grid, we apply the multigrid method as an interior iteration on the Jacobian system. Finally, we provide a proof for the L�-convergence of the Newton-multigrid method for parabolic quasi-variational inequalities with a nonlinear right-hand, by giving a numerical example for this problem. ? 2024 Ferdowsi University of Mashhad. All rights reserved. |
| format | Article |
| id | my.uniten.dspace-36140 |
| institution | Universiti Tenaga Nasional |
| publishDate | 2025 |
| publisher | Ferdowsi University of Mashhad |
| record_format | dspace |
| spelling | my.uniten.dspace-361402025-03-03T15:41:26Z A numerical solution of parabolic quasi-variational inequality nonlinear using Newton-multigrid method Bahi M. Beggas M. Nesba N. Imtiaz A. 59562493500 57211014198 59562317400 59563158700 In this article, we apply three numerical methods to study the L�convergence of the Newton-multigrid method for parabolic quasi-variational inequalities with a nonlinear right-hand side. To discretize the problem, we utilize a finite element method for the operator and Euler scheme for the time. To obtain the system discretization of the problem, we reformulate the parabolic quasi-variational inequality as a Hamilton?Jacobi?Bellman equation. For linearizing the problem on the coarse grid, we employ Newton?s method as an external interior iteration of the Jacobian system. On the smooth grid, we apply the multigrid method as an interior iteration on the Jacobian system. Finally, we provide a proof for the L�-convergence of the Newton-multigrid method for parabolic quasi-variational inequalities with a nonlinear right-hand, by giving a numerical example for this problem. ? 2024 Ferdowsi University of Mashhad. All rights reserved. Final 2025-03-03T07:41:26Z 2025-03-03T07:41:26Z 2024 Article 10.22067/IJNAO.2024.86954.1395 2-s2.0-85218097972 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85218097972&doi=10.22067%2fIJNAO.2024.86954.1395&partnerID=40&md5=7ca12cdd3df0f413c9356697f8d1dc70 https://irepository.uniten.edu.my/handle/123456789/36140 14 4 991 1015 Ferdowsi University of Mashhad Scopus |
| spellingShingle | Bahi M. Beggas M. Nesba N. Imtiaz A. A numerical solution of parabolic quasi-variational inequality nonlinear using Newton-multigrid method |
| title | A numerical solution of parabolic quasi-variational inequality nonlinear using Newton-multigrid method |
| title_full | A numerical solution of parabolic quasi-variational inequality nonlinear using Newton-multigrid method |
| title_fullStr | A numerical solution of parabolic quasi-variational inequality nonlinear using Newton-multigrid method |
| title_full_unstemmed | A numerical solution of parabolic quasi-variational inequality nonlinear using Newton-multigrid method |
| title_short | A numerical solution of parabolic quasi-variational inequality nonlinear using Newton-multigrid method |
| title_sort | numerical solution of parabolic quasi-variational inequality nonlinear using newton-multigrid method |
| url_provider | http://dspace.uniten.edu.my/ |