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The virtual element method for a minimal surface problem

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Abstract

In this paper we consider the Virtual Element discretization of a minimal surface problem, a quasi-linear elliptic partial differential equation modeling the problem of minimizing the area of a surface subject to a prescribed boundary condition. We derive an optimal error estimate and present several numerical tests assessing the validity of the theoretical results.

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Acknowledgements

The authors are members of the INdAM Research group GNCS and this work is partially funded by INDAM-GNCS. P.F.A. and M.V. acknowledge the financial support of MIUR thourgh the PRIN grant n. 201744KLJL.

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Authors and Affiliations

  1. MOX, Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Paola Francesca Antonietti & Marco Verani

  2. Istituto di Matematica Applicata e Tecnologie Informatiche - CNR, Pavia, Italy

    Silvia Bertoluzza, Daniele Prada & Marco Verani

Authors
  1. Paola Francesca Antonietti
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  2. Silvia Bertoluzza
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  3. Daniele Prada
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  4. Marco Verani
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Correspondence to Daniele Prada.

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Antonietti, P.F., Bertoluzza, S., Prada, D. et al. The virtual element method for a minimal surface problem. Calcolo 57, 39 (2020). https://doi.org/10.1007/s10092-020-00388-0

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  • DOI: https://doi.org/10.1007/s10092-020-00388-0

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