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

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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 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.

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Acknowledgements

The authors would like to thank Gabriel N. Gatica, CI2MA, and Departamento de Ingeniería Matemática, Universidad de Concepción, Chile, for his suggestions that significantly influenced the organization of this paper.

Funding

The work of Filánder A. Sequeira was partially supported by Universidad Nacional, Costa Rica, through the project 0103-18.

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  1. Escuela de Matemática, Universidad Nacional, Campus Omar Dengo, Heredia, Costa Rica

    Filánder A. Sequeira & Helen Guillén-Oviedo

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  1. Filánder A. Sequeira
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  2. Helen Guillén-Oviedo
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Correspondence to Filánder A. Sequeira.

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Sequeira, F.A., Guillén-Oviedo, H. Some aspects on the computational implementation of diverse terms arising in mixed virtual element formulations. Numer Algor 89, 487–528 (2022). https://doi.org/10.1007/s11075-021-01123-8

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