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The Virtual Element Method with curved edges

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arxiv 1711.04306 v4 pith:3I4PY73K submitted 2017-11-12 math.NA cs.NA

L. Beirão da Veiga , A. Russo , G. Vacca This is my paper
classification math.NAcs.NA
keywords curvedapproximationconvergencedomainratevirtualaccuracyboundary
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abstract

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 $k \geq 2$, 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.

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