论文标题
压力有线的Stokes元素：Scott-Vogelius元素的网状射击版本
The pressure-wired Stokes element: a mesh-robust version of the Scott-Vogelius element
论文作者
论文摘要
Scott-Vogelius有限元对2D中固定stokes方程的数值离散化是一个流行元素，它基于多项式订单$ K $的连续速度近似值和$ k-1 $ k-1的不连续压力近似。它采用“单数距离”（通过某些几何网状数量$θ\ left（\ MathBf {z} \ right）\ geq 0 $用于三角形验证$ \ mathbf {z} $），并在与vertices $ \ mathbf {z z} $ y MATH的压力空间上强加了局部侧面状况= 0 $。该方法对于任何固定的常规三角剖分和$ k \ geq 4 $都是稳定的。但是，如果三角剖分包含几乎奇异的顶点$ 0 <θ\ left（\ mathbf {z} \ right）\ ll 1 $，则inf-sup常数会恶化。 在本文中，我们引入了Scott-Vogelius元素的非常简单的参数依赖性修改，以使Inf-SUP常数独立于几乎呈斑点顶点。我们将通过分析以及数值实验表明，对离散速度的无差异条件的影响可忽略不计。
The Scott-Vogelius finite element pair for the numerical discretization of the stationary Stokes equation in 2D is a popular element which is based on a continuous velocity approximation of polynomial order $k$ and a discontinuous pressure approximation of order $k-1$. It employs a "singular distance" (measured by some geometric mesh quantity $ Θ\left( \mathbf{z}\right) \geq 0$ for triangle vertices $\mathbf{z}$) and imposes a local side condition on the pressure space associated to vertices $\mathbf{z}$ with $Θ\left( \mathbf{z}\right) =0$. The method is inf-sup stable for any fixed regular triangulation and $k\geq 4$. However, the inf-sup constant deteriorates if the triangulation contains nearly singular vertices $0<Θ\left( \mathbf{z}\right) \ll 1$. In this paper, we introduce a very simple parameter-dependent modification of the Scott-Vogelius element such that the inf-sup constant is independent of nearly-singular vertices. We will show by analysis and also by numerical experiments that the effect on the divergence-free condition for the discrete velocity is negligibly small.
