The Virtual Element Method with curved edges
2019 ◽
Vol 53
(2)
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pp. 375-404
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Keyword(s):
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.
2016 ◽
Vol 72
(8)
◽
pp. 1968-1976
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2021 ◽
Vol 386
◽
pp. 114098
2005 ◽
Vol 22
(1)
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pp. 45-56
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Keyword(s):
2018 ◽
Vol 77
(3)
◽
pp. 1874-1908
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2021 ◽
Vol 381
◽
pp. 113815
2021 ◽
Vol 375
◽
pp. 113649
Keyword(s):