Abstract Recently, the P1-nonconforming finite element space over square meshes has been proved stable to solve Stokes equations with the piecewise constant space for velocity and pressure, respectively. In this paper, we will introduce its locally divergence-free subspace to solve the elliptic problem for the velocity only decoupled from the Stokes equation. The concerning system of linear equations is much smaller compared to the Stokes equations. Furthermore, it is split into two smaller ones. After solving the velocity first, the pressure in the Stokes problem can be obtained by an explicit method very rapidly.

中文翻译：

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斯托克斯方程方格网格上的 P1 非一致性无散度有限元方法

摘要 最近，已证明正方形网格上的 P1 非一致性有限元空间可以稳定地分别求解速度和压力的分段恒定空间的 Stokes 方程。在本文中，我们将引入其局部无发散子空间来解决仅从斯托克斯方程解耦的速度的椭圆问题。与斯托克斯方程相比，相关的线性方程组要小得多。此外，它被分成两个较小的。先求解速度后，斯托克斯问题中的压力可以通过显式方法很快得到。