本文用分片线性元离散椭圆型问题。用预处理共轭梯度法求解有限元方程。

In this paper, the elliptic problems are discreted by linear elements, the finite element system are solved by PCG method.

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文末给出了应用虚拟区域法得到的线性椭圆型问题、绕固定圆柱二维定常流动的数值结果，并与贴体网格上的结果或实验结果进行了比较以验证数值方法。

Finally, we present the numerical results of a linear elliptic problem and flows around a fixed disk, and the comparison with body-fitted mesh results or experimental data.

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针对求一类特殊的椭圆型问题在任意点的数值解问题，本文在把有限元方法与蒙特卡罗方法相结合的基础上提出了一种新的高效蒙特卡罗算法，并用算例说明了该方法的优越性。

For a special elliptic problem, a new effective Monte-Carlo method is obtained in this paper, which put FEM and Monte-Carlo method together. Lastly, some numerical examples are given.

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