In this paper, a new $P_{2}-P_{1}$ finite element pair is proposed for incompressible fluid. For this pair, the discrete inf-sup condition and the discrete Korn's inequality hold on general triangulations. It yields exactly divergence-free velocity approximations when applied to models of incompressible flows. The robust capacity of the pair for incompressible flows are verified theoretically and numerically.

翻译：在本文中, 为不可压缩液体建议了一个新的 $P ⁇ 2}- P ⁇ 1} 限定元素配对 。 对于此对, 离散的内脏状况和离散的科恩的不平等性可以维持一般三角测量。 当应用到不可压缩流量模型时, 它产生完全无差异的速率近似值。 双对的坚固的不可压缩流量能力在理论上和数字上都得到验证 。