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A numerical implementation for the high-order 2D virtual element method in MATLAB

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Abstract

We present a numerical implementation for the Virtual Element Method that incorporates high order spaces. We include all the required computations in order to assemble the stiffness and mass matrices, and right hand side. Convergence of the method is verified for different polygonal partitions. An specific mesh-free application that allows to approximate harmonic functions is discussed, which is based on high-order projections onto polynomial spaces of degree k; this approach only requires to solve a k(k − 1)/2 linear system, reducing significantly the number of operations compared to usual finite or virtual element methods, and can be modified for different virtual spaces and elliptic partial differential equations.

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Acknowledgements

The authors gratefully acknowledge the institutional support for the project B8290 subscribed to the Vice-Rectory for Research, University of Costa Rica.

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Authors and Affiliations

  1. Escuela de Matemática, Universidad de Costa Rica, San José, Costa Rica

    César Herrera & Ricardo Corrales-Barquero

  2. Department of Mathematics, University of California Davis, Davis, CA, USA

    Jorge Arroyo-Esquivel

  3. CIMPA - Escuela de Matemática, Universidad de Costa Rica, San José, Costa Rica

    Juan G. Calvo

Authors
  1. César Herrera
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  2. Ricardo Corrales-Barquero
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  3. Jorge Arroyo-Esquivel
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  4. Juan G. Calvo
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Correspondence to César Herrera.

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Herrera, C., Corrales-Barquero, R., Arroyo-Esquivel, J. et al. A numerical implementation for the high-order 2D virtual element method in MATLAB. Numer Algor 92, 1707–1721 (2023). https://doi.org/10.1007/s11075-022-01361-4

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  • DOI: https://doi.org/10.1007/s11075-022-01361-4

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