Details
| Original language | English |
|---|---|
| Pages (from-to) | 44-53 |
| Number of pages | 10 |
| Journal | Computers and Mathematics with Applications |
| Volume | 136 |
| Early online date | 10 Feb 2023 |
| Publication status | Published - 15 Apr 2023 |
Abstract
In this paper, we investigate a new mixed method proposed by Rafetseder and Zulehner for Kirchhoff plates and apply it to fourth order eigenvalue problems. Using two auxiliary variables this new mixed method makes it possible to require only H1 regularity for the displacement and the auxiliary variables, without the demand of a convex domain. We provide a direct comparison, specifically in view of convergence orders, to the C0-IPG method and Ciarlet-Raviart's mixed method of vibration problems with the boundary conditions of the clamped plate and the simply supported plate. The numerical experiments are done with the open-source finite element library deal.II and include the implementation of the coupling of finite elements with elements on the boundary to incorporate non-trivial boundary conditions.
Keywords
- Biharmonic equation, Eigenvalue problem, Finite elements, Mixed method
ASJC Scopus subject areas
- Mathematics(all)
- Modelling and Simulation
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Computational Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Computers and Mathematics with Applications, Vol. 136, 15.04.2023, p. 44-53.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A new mixed method for the biharmonic eigenvalue problem
AU - Kosin, V.
AU - Beuchler, S.
AU - Wick, T.
N1 - Funding Information: This work is funded by the Deutsche Forschungsgemeinschaft (DFG) under Germany's Excellence Strategy within the Cluster of Excellence PhoenixD (EXC 2122, Project ID 390833453). The first author is currently funded in his PhD project by the Deutsch-Französische Hochschule in the Program CDFA-04-19. All authors thank Michèle Heurs (Leibniz University Hannover) and her group for discussions on thin elastic plates.
PY - 2023/4/15
Y1 - 2023/4/15
N2 - In this paper, we investigate a new mixed method proposed by Rafetseder and Zulehner for Kirchhoff plates and apply it to fourth order eigenvalue problems. Using two auxiliary variables this new mixed method makes it possible to require only H1 regularity for the displacement and the auxiliary variables, without the demand of a convex domain. We provide a direct comparison, specifically in view of convergence orders, to the C0-IPG method and Ciarlet-Raviart's mixed method of vibration problems with the boundary conditions of the clamped plate and the simply supported plate. The numerical experiments are done with the open-source finite element library deal.II and include the implementation of the coupling of finite elements with elements on the boundary to incorporate non-trivial boundary conditions.
AB - In this paper, we investigate a new mixed method proposed by Rafetseder and Zulehner for Kirchhoff plates and apply it to fourth order eigenvalue problems. Using two auxiliary variables this new mixed method makes it possible to require only H1 regularity for the displacement and the auxiliary variables, without the demand of a convex domain. We provide a direct comparison, specifically in view of convergence orders, to the C0-IPG method and Ciarlet-Raviart's mixed method of vibration problems with the boundary conditions of the clamped plate and the simply supported plate. The numerical experiments are done with the open-source finite element library deal.II and include the implementation of the coupling of finite elements with elements on the boundary to incorporate non-trivial boundary conditions.
KW - Biharmonic equation
KW - Eigenvalue problem
KW - Finite elements
KW - Mixed method
UR - http://www.scopus.com/inward/record.url?scp=85147854672&partnerID=8YFLogxK
U2 - 10.1016/j.camwa.2023.01.038
DO - 10.1016/j.camwa.2023.01.038
M3 - Article
AN - SCOPUS:85147854672
VL - 136
SP - 44
EP - 53
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
SN - 0898-1221
ER -