Crouzeix-Raviart triangular elements are inf-sup stable
Crouzeix-Raviart triangular elements are inf-sup stable
复制标题
Crouzeix-Raviart 三角形元件 inf-sup 稳定
作者：
C. Carstensen;S. Sauter
对于Stokes方程，Crouzeix-Raviart三角形有限元对于至少有一个内部顶点的任何网格都是$\inf$ - $\sup$稳定的。这一结果证实了1989年{\emCrouzeix-Falk关于}$p=3$的一个猜想{\em。我们的证明适用于}任意奇数次$p\ge 3$，因此二维中$p$次的crouzeeix - raviart三角有限元和积分消失的$p-1$次的分段多项式对{\em所有正整数形成稳定的Stokes对}$p$。
The Crouzeix-Raviart triangular finite elements are $\inf$-$\sup$ stable for the Stokes equations for any mesh with at least one interior vertex. This result affirms a {\em conjecture of Crouzeix-Falk} from 1989 for $p=3$. Our proof applies to {\em any odd degree} $p\ge 3$ and hence Crouzeix-Raviart triangular finite elements of degree $p$ in two dimensions and the piecewise polynomials of degree $p-1$ with vanishing integral form a stable Stokes pair {\em for all positive integers} $p$.