Generalized mixed and primal hybrid methods with applications to plate bending
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910763375919104 |
|---|---|
| author | Heuer, Norbert |
| author_facet | Heuer, Norbert |
| contents | We present an extended framework for hybrid finite element approximations of self-adjoint, positive definite operators. It covers the cases of primal, mixed, and ultraweak formulations, both at the continuous and discrete levels, and gives rise to conforming discretizations. Our framework allows for flexible continuity restrictions across elements, and includes the extreme cases of conforming and discontinuous hybrid methods. We illustrate an application of the framework to the Kirchhoff-Love plate pending model and present three primal hybrid and two mixed hybrid methods, four of them with numerical examples. In particular, we present conforming frameworks for (in classical meaning) non-conforming elements of Morley, Zienkiewicz triangular, and Hellan-Herrmann-Johnson types. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12541 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized mixed and primal hybrid methods with applications to plate bending Heuer, Norbert Numerical Analysis 65N30, 35J35, 74G15, 74S05, 74K20 We present an extended framework for hybrid finite element approximations of self-adjoint, positive definite operators. It covers the cases of primal, mixed, and ultraweak formulations, both at the continuous and discrete levels, and gives rise to conforming discretizations. Our framework allows for flexible continuity restrictions across elements, and includes the extreme cases of conforming and discontinuous hybrid methods. We illustrate an application of the framework to the Kirchhoff-Love plate pending model and present three primal hybrid and two mixed hybrid methods, four of them with numerical examples. In particular, we present conforming frameworks for (in classical meaning) non-conforming elements of Morley, Zienkiewicz triangular, and Hellan-Herrmann-Johnson types. |
| title | Generalized mixed and primal hybrid methods with applications to plate bending |
| topic | Numerical Analysis 65N30, 35J35, 74G15, 74S05, 74K20 |
| url | https://arxiv.org/abs/2406.12541 |