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
N1 - Publisher Copyright:
© 2021 Global-Science Press.
PY - 2021/11
Y1 - 2021/11
N2 - 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.
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.
KW - Fourth order eigenvalue problem
KW - Multi-connected planar domain
KW - Multilevel mixed element method
UR - http://www.scopus.com/inward/record.url?scp=85115811046&partnerID=8YFLogxK
U2 - 10.4208/NMTMA.OA-2021-0046
DO - 10.4208/NMTMA.OA-2021-0046
M3 - Article
AN - SCOPUS:85115811046
SN - 1004-8979
VL - 14
SP - 920
EP - 944
JO - Numerical Mathematics
JF - Numerical Mathematics
IS - 4
ER -