The $\mathtt{T}$-coercivity approach for mixed problems
Classically, the well-posedness of variational formulations of mixed linear problems is achieved through the inf-sup condition on the constraint. In this note, we propose an alternative framework to study such problems by using the $\mathtt{T}$-coercivity approach to derive a global inf-sup conditio...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.590/ |
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| _version_ | 1825206132980842496 |
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| author | Barré, Mathieu Ciarlet, Patrick |
| author_facet | Barré, Mathieu Ciarlet, Patrick |
| author_sort | Barré, Mathieu |
| collection | DOAJ |
| description | Classically, the well-posedness of variational formulations of mixed linear problems is achieved through the inf-sup condition on the constraint. In this note, we propose an alternative framework to study such problems by using the $\mathtt{T}$-coercivity approach to derive a global inf-sup condition. Generally speaking, this is a constructive approach that, in addition, drives the design of suitable approximations. As a matter of fact, the derivation of the uniform discrete inf-sup condition for the approximate problems follows easily from the study of the original problem. To support our view, we solve a series of classical mixed problems with the $\mathtt{T}$-coercivity approach. Among others, the celebrated Fortin Lemma appears naturally in the numerical analysis of the approximate problems. |
| format | Article |
| id | doaj-art-10c0f48e72d4405ba184ca725f189688 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-10c0f48e72d4405ba184ca725f1896882025-02-07T11:23:31ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G101051108810.5802/crmath.59010.5802/crmath.590The $\mathtt{T}$-coercivity approach for mixed problemsBarré, Mathieu0Ciarlet, Patrick1Inria, 1 Rue Honoré d’Estienne d’Orves, 91120 Palaiseau, France; LMS, École Polytechnique, CNRS, Institut Polytechnique de Paris, Route de Saclay, 91120 Palaiseau, FrancePOEMS, CNRS, Inria, ENSTA Paris, Institut Polytechnique de Paris, 828 Boulevard des Maréchaux, 91120 Palaiseau, FranceClassically, the well-posedness of variational formulations of mixed linear problems is achieved through the inf-sup condition on the constraint. In this note, we propose an alternative framework to study such problems by using the $\mathtt{T}$-coercivity approach to derive a global inf-sup condition. Generally speaking, this is a constructive approach that, in addition, drives the design of suitable approximations. As a matter of fact, the derivation of the uniform discrete inf-sup condition for the approximate problems follows easily from the study of the original problem. To support our view, we solve a series of classical mixed problems with the $\mathtt{T}$-coercivity approach. Among others, the celebrated Fortin Lemma appears naturally in the numerical analysis of the approximate problems.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.590/ |
| spellingShingle | Barré, Mathieu Ciarlet, Patrick The $\mathtt{T}$-coercivity approach for mixed problems Comptes Rendus. Mathématique |
| title | The $\mathtt{T}$-coercivity approach for mixed problems |
| title_full | The $\mathtt{T}$-coercivity approach for mixed problems |
| title_fullStr | The $\mathtt{T}$-coercivity approach for mixed problems |
| title_full_unstemmed | The $\mathtt{T}$-coercivity approach for mixed problems |
| title_short | The $\mathtt{T}$-coercivity approach for mixed problems |
| title_sort | mathtt t coercivity approach for mixed problems |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.590/ |
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