论文标题
$ hp $ -crouzeix-raviart三角形元素的inf-sup常数
The inf-sup constant for $hp$-Crouzeix-Raviart triangular elements
论文作者
论文摘要
在本文中，我们考虑了Crouzeix-raviart元素对二维固定stokes方程的离散化，以构成符合三角形和不连续的压力$ k-1 $的多项式订单$ k \ geq1 $的速度。我们将从下方绑定INF-SUP常数，而不是网格大小，并表明它仅取决于$ k $。我们在网格上的假设非常温和：对于奇数$ k $，我们要求三角形包含至少一个内顶点，而即使对于$ k $，我们都假设三角剖分包含一个超过一个三角形。
In this paper, we consider the discretization of the two-dimensional stationary Stokes equation by Crouzeix-Raviart elements for the velocity of polynomial order $k\geq1$ on conforming triangulations and discontinuous pressure approximations of order $k-1$. We will bound the inf-sup constant from below independent of the mesh size and show that it depends only logarithmically on $k$. Our assumptions on the mesh are very mild: for odd $k$ we require that the triangulations contain at least one inner vertex while for even $k$ we assume that the triangulations consist of more than a single triangle.
