A serendipity fully discrete div-div complex on polygonal meshes
In this work we address the reduction of face degrees of freedom (DOFs) for discrete elasticity complexes. Specifically, using serendipity techniques, we develop a reduced version of a recently introduced two-dimensional complex arising from traces of the three-dimensional elasticity complex. The ke...
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Académie des sciences
2023-03-01
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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.150/ |
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| author | Botti, Michele Di Pietro, Daniele A. Salah, Marwa |
| author_facet | Botti, Michele Di Pietro, Daniele A. Salah, Marwa |
| author_sort | Botti, Michele |
| collection | DOAJ |
| description | In this work we address the reduction of face degrees of freedom (DOFs) for discrete elasticity complexes. Specifically, using serendipity techniques, we develop a reduced version of a recently introduced two-dimensional complex arising from traces of the three-dimensional elasticity complex. The keystone of the reduction process is a new estimate of symmetric tensor-valued polynomial fields in terms of boundary values, completed with suitable projections of internal values for higher degrees. We prove an extensive set of new results for the original complex and show that the reduced complex has the same homological and analytical properties as the original one. This paper also contains an appendix with proofs of general Poincaré–Korn-type inequalities for hybrid fields. |
| format | Article |
| id | doaj-art-6faf2ab453724c959b6d2ef3b61727c1 |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2023-03-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-6faf2ab453724c959b6d2ef3b61727c12025-02-07T13:46:20ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342023-03-01351S121924910.5802/crmeca.15010.5802/crmeca.150A serendipity fully discrete div-div complex on polygonal meshesBotti, Michele0Di Pietro, Daniele A.1Salah, Marwa2MOX, Politecnico di Milano, ItalyIMAG, Univ Montpellier, CNRS, Montpellier, FranceIMAG, Univ Montpellier, CNRS, Montpellier, FranceIn this work we address the reduction of face degrees of freedom (DOFs) for discrete elasticity complexes. Specifically, using serendipity techniques, we develop a reduced version of a recently introduced two-dimensional complex arising from traces of the three-dimensional elasticity complex. The keystone of the reduction process is a new estimate of symmetric tensor-valued polynomial fields in terms of boundary values, completed with suitable projections of internal values for higher degrees. We prove an extensive set of new results for the original complex and show that the reduced complex has the same homological and analytical properties as the original one. This paper also contains an appendix with proofs of general Poincaré–Korn-type inequalities for hybrid fields.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.150/Discrete de Rham methodserendipitycompatible discretisationsmixed formulationdiv-div complexbiharmonic equationKirchhoff–Love plates |
| spellingShingle | Botti, Michele Di Pietro, Daniele A. Salah, Marwa A serendipity fully discrete div-div complex on polygonal meshes Comptes Rendus. Mécanique Discrete de Rham method serendipity compatible discretisations mixed formulation div-div complex biharmonic equation Kirchhoff–Love plates |
| title | A serendipity fully discrete div-div complex on polygonal meshes |
| title_full | A serendipity fully discrete div-div complex on polygonal meshes |
| title_fullStr | A serendipity fully discrete div-div complex on polygonal meshes |
| title_full_unstemmed | A serendipity fully discrete div-div complex on polygonal meshes |
| title_short | A serendipity fully discrete div-div complex on polygonal meshes |
| title_sort | serendipity fully discrete div div complex on polygonal meshes |
| topic | Discrete de Rham method serendipity compatible discretisations mixed formulation div-div complex biharmonic equation Kirchhoff–Love plates |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.150/ |
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