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Volume 14, Issue 4
Order Reduced Schemes for the Fourth Order Eigenvalue Problems on Multi-Connected Planar Domains

Yingxia Xi, Xia Ji & Shuo Zhang

DOI: 10.4208/nmtma.OA-2021-0046

Numer. Math. Theor. Meth. Appl., 14 (2021), pp. 920-944.

Published online: 2021-09

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  • 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.

  • Keywords

Multilevel mixed element method, fourth order eigenvalue problem, multi-connected planar domain.

  • AMS Subject Headings

65N25, 65N30, 47B07

  • Copyright

COPYRIGHT: © Global Science Press

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@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} }
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.

Xi , YingxiaJi , Xia and Zhang , Shuo. (2021). Order Reduced Schemes for the Fourth Order Eigenvalue Problems on Multi-Connected Planar Domains. Numerical Mathematics: Theory, Methods and Applications. 14 (4). 920-944. doi:10.4208/nmtma.OA-2021-0046
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