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 considers any polynomial degree k ≥ 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(div) and H¹, simultaneously. In addition, an algorithm is proposed for the assembly of the associated global linear system for Newton’s iteration. Finally, we present a numerical example in order to illustrate the performance of the mixed-VEM scheme and confirm the expected theoretical convergence rates.

在本文中，我们描述了在二维伪应力-速度公式中由混合虚拟元方法（混合 VEM）产生的一些积分项的计算实现。这里介绍的实现通过矩阵乘法和 Kronecker 乘积构建几个小尺寸的局部矩阵，以自然的方式考虑任何多项式次数k ≥ 0。特别是，我们将上述矩阵应用于具有 Dirichlet 边界条件的 Navier-Stokes 方程，其混合 VEM 公式最初是在最近的一项工作中提出并使用H (div) 和H ^{1 的}虚拟元素子空间进行分析的， 同时地。此外，还提出了一种算法，用于组装相关的全局线性系统以进行牛顿迭代。最后，我们提供了一个数值例子，以说明混合 VEM 方案的性能并确认预期的理论收敛速度。