A nonconforming P2 and discontinuous P1 mixed finite element on tetrahedral grids
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_ | 1866911995496759296 |
|---|---|
| author | Zhang, Shangyou |
| author_facet | Zhang, Shangyou |
| contents | A nonconforming $P_2$ finite element is constructed by enriching the conforming $P_2$ finite element space with seven $P_2$ nonconforming bubble functions (out of fifteen such bubble functions on each tetrahedron). This spacial nonconforming $P_2$ finite element, combined with the discontinuous $P_1$ finite element on general tetrahedral grids, is inf-sup stable for solving the Stokes equations. Consequently such a mixed finite element method produces optimal-order convergen solutions for solving the stationary Stokes equations. Numerical tests confirm the theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10227 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A nonconforming P2 and discontinuous P1 mixed finite element on tetrahedral grids Zhang, Shangyou Numerical Analysis A nonconforming $P_2$ finite element is constructed by enriching the conforming $P_2$ finite element space with seven $P_2$ nonconforming bubble functions (out of fifteen such bubble functions on each tetrahedron). This spacial nonconforming $P_2$ finite element, combined with the discontinuous $P_1$ finite element on general tetrahedral grids, is inf-sup stable for solving the Stokes equations. Consequently such a mixed finite element method produces optimal-order convergen solutions for solving the stationary Stokes equations. Numerical tests confirm the theory. |
| title | A nonconforming P2 and discontinuous P1 mixed finite element on tetrahedral grids |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2408.10227 |