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High Order FEMs Using Penalty Technigues for Poisson's Eigenvalue Problems with Periodical Boundary Conditions

Adini¡¦s elements are applied to Poisson¡¦s eigenvalue problems in the unit square with periodical boundary conditions and the leading eigenvalues are obtained from the Rayleigh quotient. The penalty techniques are developed to copy with periodical boundary conditions, and superconvergence is also explored for leading eigenvalues. The optimal convergence O(h^6) are obtained for quasiuniform elements
(see [2, 21]). When the uniform rectangular elements are used, the superconvergence O(h^6+p) with p = 1 or p = 2 of leading eigenvalues is proved, where h is the maximal boundary length of Adini¡¦s elements. Numerical experiments are carried to verify the analysis made.
Keywords. Adini¡¦s elements, Poisson¡¦s equation, periodical boundary conditions, eigenvalue problems.

Identiferoai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0626106-150814
Date26 June 2006
CreatorsJian, Shr-jie
ContributorsChien-Sen Huang, Tzon-Tzer Lu, Hung-Tsai Huang, Cheng-Sheng Chien, Zi-Cai Li
PublisherNSYSU
Source SetsNSYSU Electronic Thesis and Dissertation Archive
LanguageEnglish
Detected LanguageEnglish
Typetext
Formatapplication/pdf
Sourcehttp://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0626106-150814
Rightswithheld, Copyright information available at source archive

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