论文标题
关于3D中crouzeix-raviart Stokes元素的Inf-Sup稳定性
On the Inf-Sup Stability of Crouzeix-Raviart Stokes Elements in 3D
论文作者
论文摘要
我们考虑crouzeix-raviart型元素在三个空间维度中的固定stokes方程的不合格离散化。 M. Crouzeix和P.-A.的开创性论文中的原始定义Raviart于1973年是隐性的，还具有具体选择的实质性自由。在本文中，我们以完全明确的方式引入了3D基本的Crouzeix-raviart基础函数。我们证明，对于多项式程度$ k = 2 $（二次速度近似），用于stokes方程的基本crouzeixraviart元素是稳定的。我们确定了符合$（K; K -1）$ 3D Stokes元素的虚假压力模式，并通过使用基本的Crouzeix -Raviart空间来表明这些元素可以消除这些元素。
We consider non-conforming discretizations of the stationary Stokes equation in three spatial dimensions by Crouzeix-Raviart type elements. The original definition in the seminal paper by M. Crouzeix and P.-A. Raviart in 1973 is implicit and also contains substantial freedom for a concrete choice. In this paper, we introduce basic Crouzeix-Raviart basis functions in 3D in analogy to the 2D case in a fully explicit way. We prove that this basic CrouzeixRaviart element for the Stokes equation is inf-sup stable for polynomial degree $k =2$ (quadratic velocity approximation). We identify spurious pressure modes for the conforming $(k; k - 1)$ 3D Stokes element and show that these are eliminated by using the basic Crouzeix-Raviart space.
