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| 研究生： |
許柏翊 Po-Yi Hsu |
|---|---|
| 論文名稱： | A new approach of finding vector fields with prescribed divergence, vorticity and normal trace using the finite element method |
| 指導教授： | 鄭經斅 |
| 口試委員: | |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系 Department of Mathematics |
| 論文出版年： | 2016 |
| 畢業學年度： | 104 |
| 語文別： | 英文 |
| 論文頁數： | 25 |
| 中文關鍵詞： | 有限元素法 |
| 相關次數： | 點閱：13 下載：0 |
| 分享至: |
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在本論文中，我們討論一個經典的數學問題：要找到一個流體的速度場，使此速度場滿足所給定的散度、旋度以及流域邊界法線方向的分量。我們不直接解這個問題，而是在基於一些特定假設之下，把原本的問題變成一個比較容易找到解的偏微分方程，並且利用有限元素法找到此偏微分方程的數值解，計算其誤差以及收斂階。
In this thesis, we are concerned with a classical mathematic problem of solving for a vector field whose divergence, vorticity and normal trace are prescribed. We do not solve this problem directly; however, based on some particular assumptions, we instead transform this classical problem to another system of vector-valued partial differential equations that are essentially easier to solve. We then use the finite element method to solve this system of partial differential equations, do some numerical experiment, and study the rate of convergence.
Howard C.Elman, David J.Silvester and Andrew J.Wathen. Finite Element and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics. 2005.
Stephen H.Friedberg, Arnold J.Insel and Lawrence E.Spence. Linear Algebra. 2003.
