Title page for etd-0802105-042131


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URN etd-0802105-042131
Author Hung-Jou Shen
Author's Email Address No Public.
Statistics This thesis had been viewed 5064 times. Download 2041 times.
Department Applied Mathematics
Year 2004
Semester 2
Degree Master
Type of Document
Language English
Title Non-conforming Finite Element Methods for Eigenvalue Problems
Date of Defense 2005-05-26
Page Count 50
Keyword
  • extension of rotated bilinear element
  • rotated bilinear element
  • Wilson's element
  • bilinear element
  • linear element
  • non- conforming
  • eigenvalue
  • conforming
  • Abstract The thesis explores the new expansions of eigenvalues for -Δu =λρu in S with the Dirichlet boundary condition u=0 on $partial S$ by two conforming elements: the linear element $P_1$ and the bilinear element $Q_1$, and three non-conforming elements: the rotated bilinear element (denoted $Q_1^{rot}$), the extension of $Q_1^{rot}$ (denoted $EQ_1^{rot}$) and Wilson's element. The expansions indicate that $P_1$, $Q_1$ and $Q_1^{rot}$ provide the upper bounds of the eigenvalues, and $EQ_1^{rot}$ and Wilson's elements provide the lower bounds of the eigenvalues. Comparing the five finite elements, the $Q_1^{rot}$ element is more accurate. By the extrapolation, the superconvergence $O(h^4)$ can be obtained where $h$ is the boundary length of uniform squares. Numerical experiment are carried to verify the theoretical analysis made.
    (參照電子檔p.4)
    Advisory Committee
  • Cheng-Sheng Chien - chair
  • Tzon-Tzer Lu - co-chair
  • Hung-Tsai Huang - co-chair
  • Chien-Sen Huang - co-chair
  • Zi-Cai Li - advisor
  • Files
  • etd-0802105-042131.pdf
  • indicate access worldwide
    Date of Submission 2005-08-02

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