The Virtual Element Method for a Minimal Surface Problem

12/20/2019

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by   Paola Francesca Antonietti, et al.

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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 optimal error estimate and present several numerical tests assessing the validity of the theoretical results.