Regularization method and a posteriori error estimates for the two membranes problem
This study presents a regularization method for the two membranes problem with non-homogeneous boundary conditions. We establish both convergence results and a priori estimates for this method. Using duality theory from convex analysis, we identify the dual problem related to the two membranes probl...
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| Format: | Article |
| Language: | English |
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De Gruyter
2024-12-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2024-0116 |
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| _version_ | 1832570405748998144 |
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| author | Bouchlaghem Mohammed Mermri El Bekkaye Mellah Zhor |
| author_facet | Bouchlaghem Mohammed Mermri El Bekkaye Mellah Zhor |
| author_sort | Bouchlaghem Mohammed |
| collection | DOAJ |
| description | This study presents a regularization method for the two membranes problem with non-homogeneous boundary conditions. We establish both convergence results and a priori estimates for this method. Using duality theory from convex analysis, we identify the dual problem related to the two membranes problem. Based on this dual formulation, we give a posteriori error estimates for both the continuous and discrete versions of the problem. These a posteriori error estimates are crucial for the practical implementation of the regularized problem. |
| format | Article |
| id | doaj-art-0f9de58d34f747858d31e22ed3ef08b6 |
| institution | Kabale University |
| issn | 2391-5455 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj-art-0f9de58d34f747858d31e22ed3ef08b62025-02-02T15:46:01ZengDe GruyterOpen Mathematics2391-54552024-12-0122165966210.1515/math-2024-0116Regularization method and a posteriori error estimates for the two membranes problemBouchlaghem Mohammed0Mermri El Bekkaye1Mellah Zhor2Department of Mathematics, Faculty of Science, Mohammed Premier University, Boulevard Mohammed VI, Oujda 60050, MoroccoDepartment of Mathematics, Faculty of Science, Mohammed Premier University, Boulevard Mohammed VI, Oujda 60050, MoroccoDepartment of Mathematics, Faculty of Science, Mohammed Premier University, Boulevard Mohammed VI, Oujda 60050, MoroccoThis study presents a regularization method for the two membranes problem with non-homogeneous boundary conditions. We establish both convergence results and a priori estimates for this method. Using duality theory from convex analysis, we identify the dual problem related to the two membranes problem. Based on this dual formulation, we give a posteriori error estimates for both the continuous and discrete versions of the problem. These a posteriori error estimates are crucial for the practical implementation of the regularized problem.https://doi.org/10.1515/math-2024-0116variational inequalitiestwo membranes problema posteriori error estimatesregularization methodduality theory65k1549j4049m29 |
| spellingShingle | Bouchlaghem Mohammed Mermri El Bekkaye Mellah Zhor Regularization method and a posteriori error estimates for the two membranes problem Open Mathematics variational inequalities two membranes problem a posteriori error estimates regularization method duality theory 65k15 49j40 49m29 |
| title | Regularization method and a posteriori error estimates for the two membranes problem |
| title_full | Regularization method and a posteriori error estimates for the two membranes problem |
| title_fullStr | Regularization method and a posteriori error estimates for the two membranes problem |
| title_full_unstemmed | Regularization method and a posteriori error estimates for the two membranes problem |
| title_short | Regularization method and a posteriori error estimates for the two membranes problem |
| title_sort | regularization method and a posteriori error estimates for the two membranes problem |
| topic | variational inequalities two membranes problem a posteriori error estimates regularization method duality theory 65k15 49j40 49m29 |
| url | https://doi.org/10.1515/math-2024-0116 |
| work_keys_str_mv | AT bouchlaghemmohammed regularizationmethodandaposteriorierrorestimatesforthetwomembranesproblem AT mermrielbekkaye regularizationmethodandaposteriorierrorestimatesforthetwomembranesproblem AT mellahzhor regularizationmethodandaposteriorierrorestimatesforthetwomembranesproblem |