The purpose of the present paper is to develop C1 Virtual Elements in three dimensions for linear elliptic fourth order problems, motivated by the difficulties that standard conforming Finite Elements encounter in this framework. We focus the presentation on the lowest order case, the generalization to higher orders being briefly provided in the Appendix. The degrees of freedom of the proposed scheme are only 4 per mesh vertex, representing function values and gradient values. Interpolation error estimates for the proposed space are provided, together with a set of numerical tests to validate the method at the practical level.

Beirao da Veiga, L., Dassi, F., Russo, A. (2020). A C1 Virtual Element Method on polyhedral meshes. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 79(7), 1936-1955 [10.1016/j.camwa.2019.06.019].

A C1 Virtual Element Method on polyhedral meshes

Beirao da Veiga L.;Dassi F.
;
Russo A.
2020

Abstract

The purpose of the present paper is to develop C1 Virtual Elements in three dimensions for linear elliptic fourth order problems, motivated by the difficulties that standard conforming Finite Elements encounter in this framework. We focus the presentation on the lowest order case, the generalization to higher orders being briefly provided in the Appendix. The degrees of freedom of the proposed scheme are only 4 per mesh vertex, representing function values and gradient values. Interpolation error estimates for the proposed space are provided, together with a set of numerical tests to validate the method at the practical level.
Articolo in rivista - Articolo scientifico
Bi-Laplacian problem; C1 regularity; Polyhedral meshes; Virtual Element Method;
English
4-lug-2019
2020
79
7
1936
1955
open
Beirao da Veiga, L., Dassi, F., Russo, A. (2020). A C1 Virtual Element Method on polyhedral meshes. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 79(7), 1936-1955 [10.1016/j.camwa.2019.06.019].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/241518
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