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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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