The thesis explores the new expansions of eigenvalues for -£Gu =£f£lu 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.
(°Ñ·Ó¹q¤lÀÉp.4)
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0802105-042131 |
| Date | 02 August 2005 |
| Creators | Shen, Hung-Jou |
| Contributors | Chien-Sen Huang, Hung-Tsai Huang, Zi-Cai Li, Tzon-Tzer Lu, Cheng-Sheng Chien |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0802105-042131 |
| Rights | unrestricted, Copyright information available at source archive |
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