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 - <p style="text-align: justify;">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.</p>