The Virtual Element Method with curved edges

By L. Beirão da Veiga, Alessandro Russo, Giuseppe Vacca. ESAIM: Mathematical Modelling and Numerical Analysis, 2017

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In this paper we initiate the investigation of Virtual Elements with curved faces. We consider the case of a fixed curved boundary in two dimensions, as it happens in the approximation of problems posed on a curved domain or with a curved interface. While an approximation of the domain with polygons leads, for degree of accuracy k≥2, to a sub-optimal rate of convergence, we show (both theoretically and numerically) that the proposed curved VEM lead to an optimal rate of convergence.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/10a129f6aecd105ed409fea6a6d7474c41d61aa6