A C1 Virtual Element Method on polyhedral meshes. (1st April 2020)

• Record Type: Journal Article
• Authors: Beirão da Veiga, L.; Dassi, F.; Russo, A.
• Is Part Of: Computers & mathematics with applications. Volume 79:issue 7(2020)
• Page Start: 1936
• Page End: 1955
• Publication Date: 2020-04-01
• Subjects: Virtual Element Method -- Polyhedral meshes -- Bi-Laplacian problem -- C1 regularity; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2019.06.019
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: The purpose of the present paper is to develop C 1 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.