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Mathematics > Numerical Analysis

arXiv:1808.01105 (math)
[Submitted on 3 Aug 2018 (v1), last revised 3 Sep 2019 (this version, v3)]

Title:$C^1$ Virtual Element Method on polyhedral meshes

Authors:Lourenco Beirão da Veiga, Franco Dassi, Alessandro Russo
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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.
Comments: Computer & Mathematics with Applications (Jul 2019)
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:1808.01105 [math.NA]
  (or arXiv:1808.01105v3 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1808.01105
Related DOI: https://doi.org/10.1016/j.camwa.2019.06.019

Submission history

From: Franco Dassi [view email]
[v1] Fri, 3 Aug 2018 07:42:38 UTC (1,168 KB)
[v2] Thu, 31 Jan 2019 14:44:59 UTC (1,169 KB)
[v3] Tue, 3 Sep 2019 08:15:56 UTC (1,518 KB)
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