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

• Main Authors: Shr-jie Jian, 簡士傑
• Other Authors: Hung-Tsai Huang
• Format: Others
• Language: en_US
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/25656404801935988332

碩士 === 國立中山大學 === 應用數學系研究所 === 94 === 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.