Volume 53, Number 2, March–April 2019
|Page(s)||375 - 404|
|Published online||16 April 2019|
The Virtual Element Method with curved edges
Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Via R. Cozzi 55, 20125 Milano, Italy
2 IMATI-CNR Pavia, Via Ferrata 1, 27100 Pavia, Italy
* Corresponding author: email@example.com
Accepted: 14 September 2018
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.
Mathematics Subject Classification: 65N15 / 65N30
Key words: Virtual element method / polygonal meshes / curved elements
© EDP Sciences, SMAI 2019
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