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
Beirão da Veiga, L., Russo, A., Vacca, G. (2019). The Virtual Element Method with curved edges. MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE, 53(2), 375-404 [10.1051/m2an/2018052].
The Virtual Element Method with curved edges
Beirão da Veiga, L;Russo, A;Vacca, G
2019
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 ≥ 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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