TY - JOUR T1 - Order Reduced Schemes for the Fourth Order Eigenvalue Problems on Multi-Connected Planar Domains AU - Xi , Yingxia AU - Ji , Xia AU - Zhang , Shuo JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 920 EP - 944 PY - 2021 DA - 2021/09 SN - 14 DO - http://doi.org/10.4208/nmtma.OA-2021-0046 UR - https://global-sci.org/intro/article_detail/nmtma/19524.html KW - Multilevel mixed element method, fourth order eigenvalue problem, multi-connected planar domain. AB -

In this paper, we study the order reduced finite element method for the fourth order eigenvalue problems on multi-connected planar domains. Particularly, we take the biharmonic and the Helmholtz transmission eigenvalue problems as model problems, present for each an equivalent order reduced formulation and a corresponding stable discretization scheme, and present rigorous theoretical analysis. The schemes are readily fit for multilevel correction algorithms with optimal computational costs. Numerical experiments are given for verifications.