有限元病态时的几个异常现象

有限元病态时的一般表现是计算精度的下降和迭代费用的增加，但病态时还有些异常现象未引起足够重视。设计了固有病态和网格病态两个算例，通过Q4单元的数值结果指出，当问题病态到一定程度时，单元节点编号的不同、方程组解法的不同、对模型的等效变换等，都可能导致计算结果的明显差异，这些需要在实际使用中引起注意并进行必要的测试。

Some Unusual Phenomena in Ill-conditioned FEM

Lower precision and more iterations are generally noticed when FEM is ill-conditioned, but some other unusual phenomena have not caused sufficient attention or even been ignored. This paper designs two examples of natural ill-condition and mesh ill-condition respectively, and points out by element Q4＇s numerical results that when FEM is ill-conditioned to a certain degree, different node numbering, different equation solver, equivalent transformation of the model, etc, are all likely to lead to evidently different results, which should be paid attention in practical FEM analysis and necessary tests should be conducted.