论文标题
低阶无差异h（div） - 符合stokes流量的有限元方法
A low order divergence-free H(div)-conforming finite element method for Stokes flows
论文作者
论文摘要
在本文中，我们提出了一个$ {p_ {1}^{c}} \ oplus {rt0} -p0 $在两个/三维（2D/3D）中的普通简单网格上的stokes方程式离散化，从而产生一个确切的无差异和压力依赖性效率的效率均可取得差异。我们的方法具有以下功能。首先，我们方法的自由度的全球数量与低阶Bernardi and Raugel（$ b $ - $ r $）有限元方法（Bernardi and Raugel，1985）相同，而前者的{non-Zero条目}的数量约为后者的一半。其次，$ {p_ {1}^{c}} $速度的组成部分，速度的$ rt0 $组成部分和压力似乎可以解决流行的$ {p_ {1}^{c}}}}}}} - {rt0}} -p0 $ {rt0} -p0 $ invetrization poroelastic-type-typepe typepe typepe type typepe。最后，我们的方法可以轻松地转化为压力稳定的$ {p_ {p_ {1}^{c}}} - P0 $ p0 $ ivevetization通过$ rt0 $ component的静态冷凝问题，该分支机构的静态凝结，该组件的全局自由度少得多。还提供了说明我们方法鲁棒性的数值实验。
In this paper, we propose a ${ P_{1}^{c}}\oplus {RT0}-P0$ discretization of the Stokes equations on general simplicial meshes in two/three dimensions (2D/3D), which yields an exactly divergence-free and pressure-independent velocity approximation with optimal order. Our method has the following features. Firstly, the global number of the degrees of freedom of our method is the same as the low order Bernardi and Raugel ($B$-$R$) finite element method (Bernardi and Raugel, 1985), while the number of {the non-zero entries} of the former is about half of the latter in the velocity-velocity region of the coefficient matrix. Secondly, the ${ P_{1}^{c}}$ component of the velocity, the $RT0$ component of the velocity and the pressure seem to solve a popular ${ P_{1}^{c}}-{RT0}-P0$ discretization of a poroelastic-type system formally. Finally, our method can be easily transformed into a pressure-robust and stabilized ${ P_{1}^{c}}-P0$ discretization for the Stokes problem via the static condensation of the $RT0$ component, which has a much smaller number of global degrees of freedom. Numerical experiments illustrating the robustness of our method are also provided.
