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Student Number 952201028 Author Shih-Chao Kao(高仕超) Author's Email Address 952201028@cc.ncu.edu.tw Statistics This thesis had been viewed 1528 times. Download 645 times. Department Mathematics Year 2007 Semester 2 Degree Master Type of Document Master's Thesis Language English Title Some Residual-Free Bubble Enrichment Least-Squares Finite Element Method for the Convection-Diffusion Equation Date of Defense 2008-06-26 Page Count 31 Keyword convection-diffusion equation finite element method least-squares residual-free bubble Abstract In this thesis, we formulate the least-squares finite element method using piececewise linears to solve the convection-diffusion equation which is convection-dominated and we find that the solution is diffusive and the classical mesh refinement for the least-squares finite element method is not an economical method. Then we use the

residual-free bubble method to enrich the least-squares finite element method. This is a new application of residual-free bubble method and we solve some test problems. The numerical results show that the residual-feee bubble method for the least-squares finite element method has a good effect of enrichment。Table of Content 中文摘要.................................................i

英文摘要................................................ii

致謝詞.................................................iii

目錄....................................................iv

圖目錄...................................................v

表目錄..................................................vi

1.Introduction...........................................2

2. The LSFEM for the convection-diffusion equation.......4

3. The LSFEM enriched by a residual-free bubble method...8

3.1. Analytical approach............................... 13

3.2. Numerical approach.................................15

4. Numerical results....................................16

5. Conclusion...........................................29

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