橢圓介面方程的數值研究

Abstract

本文利用新的任意高階精度內嵌介面方法計算橢圓界面方程，並且應用至有介面的熱方程問題，我們推導出四階精度公式和測試數值結果。本方法的優點是容易應用於其他問題並且使數值精確度有顯著的改善。

In this thesis, we introduce an arbitrary high-order immersed interface method for solving elliptic equations and apply it to solve heat equation with interface. We have derived fourth-order scheme and tested in examples. The advantage of method in this thesis is easy to apply to other problems, such as two-phase flow and leads to a significant improvement in accuracy.