@Article{NMTMA-14-920, author = {Xi , YingxiaJi , Xia and Zhang , Shuo}, title = {Order Reduced Schemes for the Fourth Order Eigenvalue Problems on Multi-Connected Planar Domains}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2021}, volume = {14}, number = {4}, pages = {920--944}, abstract = {

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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2021-0046}, url = {http://global-sci.org/intro/article_detail/nmtma/19524.html} }