The Virtual Element Method with curved edges
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 2, pp. 375-404.

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.

DOI : 10.1051/m2an/2018052
Classification : 65N15, 65N30
Mots-clés : Virtual element method, polygonal meshes, curved elements
Beirão da Veiga, L. 1 ; Russo, A. 1 ; Vacca, G. 1

1 
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Beirão da Veiga, L.; Russo, A.; Vacca, G. The Virtual Element Method with curved edges. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 2, pp. 375-404. doi : 10.1051/m2an/2018052. http://www.numdam.org/articles/10.1051/m2an/2018052/

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