In this paper, we tackle the problem of constructing conforming Virtual Element spaces on polygons with curved edges. Unlike previous VEM approaches for curvilinear elements, the present construction ensures that the local VEM spaces contain all the polynomials of a given degree, thus providing the full satisfaction of the patch test. Moreover, unlike standard isoparametric FEM, this approach allows to deal with curved edges at an intermediate scale, between the small scale (treatable by homogenization) and the bigger one (where a finer mesh would make the curve flatter and flatter). The proposed method is supported by theoretical analysis and numerical tests.

Beirao Da Veiga, L., Brezzi, F., Marini, L., Russo, A. (2020). Polynomial preserving virtual elements with curved edges. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 30(8), 1555-1590 [10.1142/S0218202520500311].

### Polynomial preserving virtual elements with curved edges

#### Abstract

In this paper, we tackle the problem of constructing conforming Virtual Element spaces on polygons with curved edges. Unlike previous VEM approaches for curvilinear elements, the present construction ensures that the local VEM spaces contain all the polynomials of a given degree, thus providing the full satisfaction of the patch test. Moreover, unlike standard isoparametric FEM, this approach allows to deal with curved edges at an intermediate scale, between the small scale (treatable by homogenization) and the bigger one (where a finer mesh would make the curve flatter and flatter). The proposed method is supported by theoretical analysis and numerical tests.
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Articolo in rivista - Articolo scientifico
curved edges; patch test; Virtual elements
English
2020
30
8
1555
1590
reserved
Beirao Da Veiga, L., Brezzi, F., Marini, L., Russo, A. (2020). Polynomial preserving virtual elements with curved edges. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 30(8), 1555-1590 [10.1142/S0218202520500311].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10281/297245`