Network element methods for linear elasticity
We explain how to derive a network element for the linear elasticity problem. After presenting sufficient conditions on the network for the validity of a discrete Korn inequality, we also propose several variations of the presented method and in particular we explain how it can be used on meshes to...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-12-01
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| Series: | Comptes Rendus. Mécanique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.231/ |
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| _version_ | 1825206030306377728 |
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| author | Coatléven, Julien |
| author_facet | Coatléven, Julien |
| author_sort | Coatléven, Julien |
| collection | DOAJ |
| description | We explain how to derive a network element for the linear elasticity problem. After presenting sufficient conditions on the network for the validity of a discrete Korn inequality, we also propose several variations of the presented method and in particular we explain how it can be used on meshes to derive schemes that remain stable while keeping the stencil as compact as possible. Numerical examples illustrate the good behavior of the method, in both the mesh-based and truly meshless contexts. |
| format | Article |
| id | doaj-art-b3012ff11a9f439183495d9849fe6939 |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-b3012ff11a9f439183495d9849fe69392025-02-07T13:46:20ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342023-12-01351S133135610.5802/crmeca.23110.5802/crmeca.231Network element methods for linear elasticityCoatléven, Julien0https://orcid.org/0000-0002-4877-2558IFP Énergies nouvelles, 1 et 4 avenue de Bois-Préau, 92852 Rueil-Malmaison, FranceWe explain how to derive a network element for the linear elasticity problem. After presenting sufficient conditions on the network for the validity of a discrete Korn inequality, we also propose several variations of the presented method and in particular we explain how it can be used on meshes to derive schemes that remain stable while keeping the stencil as compact as possible. Numerical examples illustrate the good behavior of the method, in both the mesh-based and truly meshless contexts.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.231/Meshless methodsLinear elasticityVariational methods |
| spellingShingle | Coatléven, Julien Network element methods for linear elasticity Comptes Rendus. Mécanique Meshless methods Linear elasticity Variational methods |
| title | Network element methods for linear elasticity |
| title_full | Network element methods for linear elasticity |
| title_fullStr | Network element methods for linear elasticity |
| title_full_unstemmed | Network element methods for linear elasticity |
| title_short | Network element methods for linear elasticity |
| title_sort | network element methods for linear elasticity |
| topic | Meshless methods Linear elasticity Variational methods |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.231/ |
| work_keys_str_mv | AT coatlevenjulien networkelementmethodsforlinearelasticity |