Nonconforming Linear Element Method for a Generalized Tensor-Valued Stokes Equation with Application to the Triharmonic Equation
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915576639651840 |
|---|---|
| author | Gu, Ziwen Huang, Xuehai |
| author_facet | Gu, Ziwen Huang, Xuehai |
| contents | A nonconforming linear element method is developed for a three-dimensional generalized tensor-valued Stokes equation associated with the Hessian complex in this paper. A discrete Helmholtz decomposition for the piecewise constant space of traceless tensors is established, ensuring the well-posedness of the nonconforming method, and optimal error estimates are derived. Building on this, a low-order decoupled finite element method for the three-dimensional triharmonic equation is constructed by combining the Morley-Wang-Xu element methods for the biharmonic subproblems with the proposed nonconforming linear element method. Numerical experiments confirm the theoretical convergence rates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22125 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonconforming Linear Element Method for a Generalized Tensor-Valued Stokes Equation with Application to the Triharmonic Equation Gu, Ziwen Huang, Xuehai Numerical Analysis 65N30, 65N12, 65N22 A nonconforming linear element method is developed for a three-dimensional generalized tensor-valued Stokes equation associated with the Hessian complex in this paper. A discrete Helmholtz decomposition for the piecewise constant space of traceless tensors is established, ensuring the well-posedness of the nonconforming method, and optimal error estimates are derived. Building on this, a low-order decoupled finite element method for the three-dimensional triharmonic equation is constructed by combining the Morley-Wang-Xu element methods for the biharmonic subproblems with the proposed nonconforming linear element method. Numerical experiments confirm the theoretical convergence rates. |
| title | Nonconforming Linear Element Method for a Generalized Tensor-Valued Stokes Equation with Application to the Triharmonic Equation |
| topic | Numerical Analysis 65N30, 65N12, 65N22 |
| url | https://arxiv.org/abs/2510.22125 |