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.
The Virtual Element Method with curved edges
L Beirao Da Veiga;A Russo;
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.File in questo prodotto:
File | Dimensione | Formato | |
---|---|---|---|
prod_408256-doc_153037.pdf
accesso aperto
Descrizione: The Virtual Element Method with curved edges
Tipologia:
Versione Editoriale (PDF)
Dimensione
1.9 MB
Formato
Adobe PDF
|
1.9 MB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.