A new mixed method for the biharmonic eigenvalue problem
- authored by
- V. Kosin, S. Beuchler, T. Wick
- 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.
- Organisation(s)
-
Institute of Applied Mathematics
PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines
- External Organisation(s)
-
Université Paris-Saclay
- Type
- Article
- Journal
- Computers and Mathematics with Applications
- Volume
- 136
- Pages
- 44-53
- No. of pages
- 10
- ISSN
- 0898-1221
- Publication date
- 15.04.2023
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Modelling and Simulation, Computational Theory and Mathematics, Computational Mathematics
- Electronic version(s)
-
https://doi.org/10.1016/j.camwa.2023.01.038 (Access:
Closed)
