论文标题
一个有限元的家族在三个维度
A family of finite element Stokes complexes in three dimensions
论文作者
论文摘要
我们在三维空间中的四面体网格上构建有限元stoks compleveres。在最低顺序的情况下，综合体中的有限元分别具有4、18、16和1度的自由度。结果，我们获得了适合复合物的四面体上的gradcurl构成有限元和稳定的stable stokes对。我们表明，新的元素导致用于解决Gradcurl模型问题的收敛算法，并以精确的无差异条件求解Stokes系统。我们通过数值实验证明了算法的有效性。
We construct finite element Stokes complexes on tetrahedral meshes in three-dimensional space. In the lowest order case, the finite elements in the complex have 4, 18, 16, and 1 degrees of freedom, respectively. As a consequence, we obtain gradcurl-conforming finite elements and inf-sup stable Stokes pairs on tetrahedra which fit into complexes. We show that the new elements lead to convergent algorithms for solving a gradcurl model problem as well as solving the Stokes system with precise divergence-free condition. We demonstrate the validity of the algorithms by numerical experiments.
