The Stokes complex for Virtual Elements in three dimensions
The Stokes complex for Virtual Elements in three dimensions
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DOI：
10.1142/s0218202520500128
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发表时间：
2019-05
影响因子：
3.5
通讯作者：
L. Veiga;F. Dassi;G. Vacca
中科院分区：
文献类型：
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作者：
L. Veiga;F. Dassi;G. Vacca
本文有两个目的。一方面，我们开发和测试了三维的无发散虚拟元，对于可变的“多项式”阶。这些是二维无散度VEM元素的自然扩展，并进行了一些修改，以提高计算效率。我们对Stokes方程和（扩散主导的）Navier-Stokes方程测试了元件的性能。第二个，也许是主要的动机，是为了表明我们的方案，同样是三维的，具有一个潜在的离散斯托克斯复杂结构。我们建立了一对基于一般多面体划分的虚拟离散空间，第一个是标量空间，第二个是矢量空间，这样当与我们的速度和压力空间耦合时，就产生了一个离散的Stokes复。
This paper has two objectives. On one side, we develop and test numerically divergence-free Virtual Elements in three dimensions, for variable “polynomial” order. These are the natural extension of the two-dimensional divergence-free VEM elements, with some modification that allows for a better computational efficiency. We test the element’s performance both for the Stokes and (diffusion dominated) Navier–Stokes equation. The second, and perhaps main, motivation is to show that our scheme, also in three dimensions, enjoys an underlying discrete Stokes complex structure. We build a pair of virtual discrete spaces based on general polytopal partitions, the first one being scalar and the second one being vector valued, such that when coupled with our velocity and pressure spaces, yield a discrete Stokes complex.