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: firstname.lastname@example.org
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.