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arXiv · 2012.06942

Some aspects on the computational implementation of diverse terms arising in mixed virtual element formulations

Filánder A. Sequeira·Helen Guillén-Oviedo
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Abstract

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.

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Filánder A. Sequeira, Helen Guillén-Oviedo. 2020-12-13. Some aspects on the computational implementation of diverse terms arising in mixed virtual element formulations. https://arxiv.org/abs/2012.06942

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