In this paper, we propose a ${ P_{1}^{c}}\oplus {RT0}-P0$ discretization of the Stokes equations on general simplicial meshes in two/three dimensions (2D/3D), which yields an exactly divergence-free and pressure-independent velocity approximation with optimal order. Our method has the following features. Firstly, the global number of the degrees of freedom of our method is the same as the low order Bernardi and Raugel ($B$-$R$) finite element method (Bernardi and Raugel, 1985), while the number of {the non-zero entries} of the former is about half of the latter in the velocity-velocity region of the coefficient matrix. Secondly, the ${ P_{1}^{c}}$ component of the velocity, the $RT0$ component of the velocity and the pressure seem to solve a popular ${ P_{1}^{c}}-{RT0}-P0$ discretization of a poroelastic-type system formally. Finally, our method can be easily transformed into a pressure-robust and stabilized ${ P_{1}^{c}}-P0$ discretization for the Stokes problem via the static condensation of the $RT0$ component, which has a much smaller number of global degrees of freedom. Numerical experiments illustrating the robustness of our method are also provided.
翻译：在本文中,我们建议用${P ⁇ 1 ⁇ c ⁇ c ⁇ opl {RT0}-P0美元将一般简化模模模模模模的2/3维度(2D/3D)上的斯托克斯方程式分解为2/3维(2D/3D),该方程式产生完全无差异和无压力且按最佳顺序独立的速度近似。我们的方法有以下特点。首先,我们方法的自由度全球数量与伯纳迪和劳杰尔(B$-R$)的低顺序(Bernardi和Raugel,1985年)的限定元素法相同,而前者的非零条目数量约为后者的一半,在系数矩阵的高速区域中。第二,速度的${P ⁇ 1 ⁇ c ⁇ c$组成部分,速度和压力的值似乎能解决一个受欢迎的 ${P ⁇ 1 ⁇ c ⁇ {{{{{B_}-P$(B$_R$_美元)-P0元的离散化度方法。最后,我们的方法可以很容易转换成一个压力-硬度-硬度的硬度的硬度实验, 也就是的硬度方法。
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