In this work, we propose an extension of the mixed Virtual Element Method (VEM) for bi-dimensional computational grids with curvilinear edge elements. The approximation by means of rectilinear edges of a domain with curvilinear geometrical feature, such as a portion of domain boundary or an internal interface, may introduce a geometrical error that degrades the expected order of convergence of the scheme. In the present work a suitable VEM approximation space is proposed to consistently handle curvilinear geometrical objects, thus recovering optimal convergence rates. The resulting numerical scheme is presented along with its theoretical analysis and several numerical test cases to validate the proposed approach.

Dassi, F., Fumagalli, A., Losapio, D., Scialò, S., Scotti, A., Vacca, G. (2021). The mixed virtual element method on curved edges in two dimensions. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 386(1 December 2021) [10.1016/j.cma.2021.114098].

The mixed virtual element method on curved edges in two dimensions

Dassi, Franco
;
2021

Abstract

In this work, we propose an extension of the mixed Virtual Element Method (VEM) for bi-dimensional computational grids with curvilinear edge elements. The approximation by means of rectilinear edges of a domain with curvilinear geometrical feature, such as a portion of domain boundary or an internal interface, may introduce a geometrical error that degrades the expected order of convergence of the scheme. In the present work a suitable VEM approximation space is proposed to consistently handle curvilinear geometrical objects, thus recovering optimal convergence rates. The resulting numerical scheme is presented along with its theoretical analysis and several numerical test cases to validate the proposed approach.
Articolo in rivista - Articolo scientifico
Curved edges; High order approximations; Mixed VEM;
English
Dassi, F., Fumagalli, A., Losapio, D., Scialò, S., Scotti, A., Vacca, G. (2021). The mixed virtual element method on curved edges in two dimensions. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 386(1 December 2021) [10.1016/j.cma.2021.114098].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/352497
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