最小平方有限元素法求解對流擴散方程以及使用Bubble函數的改良

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高仕超(Shih-Chao Kao) 查詢紙本館藏

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數學系

論文名稱

最小平方有限元素法求解對流擴散方程以及使用Bubble函數的改良
(Some Residual-Free Bubble Enrichment Least-Squares Finite Element Method for the Convection-Diffusion Equation)

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摘要(中)

在本篇論文中，我們使用最小平方有限元素法來求解對流擴散方程中的對流佔優問題，發現到最小平方有限元素法中使用線性基底函數來求解對流佔優問題，其所求得的解並不理想，而傳統的網格加密的方法對最小平方有限元素法並不ㄧ個經濟的方法，因此我們使用RFB 方法對最小平方有限元素法進行改良的工作，這是ㄧ個新的應用。而數值結果顯示這個新的方法對於求解對流佔優問題有相當不錯的改良效果。

摘要(英)

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。

關鍵字(中)

★ 最小平方
★ 有限元素法
★ 對流擴散方程式
★ Residual-free bubble

關鍵字(英)

★ least-squares
★ finite element method
★ residual-free bubble
★ convection-diffusion equation

論文目次

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
Reference...............................................29

參考文獻

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指導教授

黃楓南(Feng-Nan Hwang)

審核日期

2008-7-16

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