论文标题
在混合虚拟元素配方中产生的各种术语的计算实施方面
Some aspects on the computational implementation of diverse terms arising in mixed virtual element formulations
论文作者
论文摘要
在本文中，我们描述了某些积分术语的计算实现，这些术语是由二维伪级速度公式中的混合虚拟元素方法（混合VEM）产生的。这里提出的实现通过自然方式考虑任何多项式$ k \ geq 0 $，通过通过矩阵乘法和kronecker产品来构建几个小型的本地矩阵。特别是，我们将上述提到的矩阵应用于具有Dirichlet边界条件的Navier-Stokes方程，该方程最初是在使用虚拟元素子空间（\ text {div}）$和$ h^1 $的最近的虚拟元素子空间中提出和分析的。此外，为牛顿迭代的相关全局线性系统组装提出了一种算法。最后，我们提出了一个数值示例，以说明混合VEM方案的性能并确认预期的理论收敛速率。
In the present paper we describe the computational implementation of some integral terms that arise from mixed virtual element methods (mixed-VEM) in two-dimensional pseudostress-velocity formulations. The implementation presented here consider any polynomial degree $k \geq 0$ in a natural way by building several local matrices of small size through the matrix multiplication and the Kronecker product. In particular, we apply the foregoing mentioned matrices to the Navier-Stokes equations with Dirichlet boundary conditions, whose mixed-VEM formulation was originally proposed and analyzed in a recent work using virtual element subspaces for $H(\text{div})$ and $H^1$, simultaneously. In addition, an algorithm is proposed for the assembly of the associated global linear system for the Newton's iteration. Finally, we present a numerical example in order to illustrate the performance of the mixed-VEM scheme and confirming the expected theoretical convergence rates.
