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