本文使用受束制之移動最小二乘法分析二維柏松方程式包括穩態熱傳問題及理想流體問題。本文方法在建立局部近似函數的同時，使其滿足控制方程式及邊界條件，利用移動最小二乘法，考慮節點上函數之殘值，建立殘值二次式，使其最小化，可得到以節點上函數值表示之近似函數，再利用各節點函數值之一致性條件以及置點法建立聯立方程式求解。
數值範例中求解了各種不同邊界條件之柏松方程式問題，將數值結果與解析解進行比較，驗證本文方法之精度及收斂率，並探討了不同邊界條件對數值精度之影響。

In this thesis, the constrained moving least square method is adopted to solve the two-dimensional Poisson’s equations, including the steady-state heat transfer and ideal fluid problems. The feature of this approach is that, by adding suitable constraints with the help of the moving least square approach, the approximate function is constrained to fit the governing equation and boundary conditions. Moreover, the weighted sum of the residuals, which results from the approximation of the field variable, is attempted to be minimized so that the process leads to an interpolation function which is expressed in terms of nodal value of the field variable. The point collocation technique is then introduced to determine the unknown nodal values.
In the numerical examples, the Poisson’s equations with different boundary conditions are solved and compared with the exact solutions to examine the accuracy and the rate of convergence of the present method. Moreover the influences of boundary conditions to the numerical accuracy are discussed.

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