A virtual element formulation for general element shapes

authored by: Peter Wriggers, Blaz Hudobivnik, Fadi Aldakheel
Abstract: The virtual element method is a lively field of research, in which considerable progress has been made during the last decade and applied to many problems in physics and engineering. The method allows ansatz function of arbitrary polynomial degree. However, one of the prerequisite of the formulation is that the element edges have to be straight. In the literature there are several new formulations that introduce curved element edges. These virtual elements allow for specific geometrical forms of the course of the curve at the edges. In this contribution a new methodology is proposed that allows to use general mappings for virtual elements which can model arbitrary geometries.
Organisation(s): Institute of Continuum Mechanics
Type: Article
Journal: Computational Mechanics
Volume: 66
Pages: 963-977
No. of pages: 15
ISSN: 0178-7675
Publication date: 10.2020
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-020-01891-5 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{edccac6ce95b4bed96dbd00a0f75c94e,
title = "A virtual element formulation for general element shapes",
abstract = "The virtual element method is a lively field of research, in which considerable progress has been made during the last decade and applied to many problems in physics and engineering. The method allows ansatz function of arbitrary polynomial degree. However, one of the prerequisite of the formulation is that the element edges have to be straight. In the literature there are several new formulations that introduce curved element edges. These virtual elements allow for specific geometrical forms of the course of the curve at the edges. In this contribution a new methodology is proposed that allows to use general mappings for virtual elements which can model arbitrary geometries.",
keywords = "Bezier splines, Isoparametric maps, Stabilization, Virtual element method",
author = "Peter Wriggers and Blaz Hudobivnik and Fadi Aldakheel",
note = "Funding Information: Open Access funding provided by Projekt DEAL. The first author gratefully acknowledges support for this research by the “German Research Foundation” (DFG) in the collaborative research center CRC 1153 “Process chain for the production of hybrid high-performance components through tailored forming” while the third author acknowledges support for this research by the Priority Program SPP 2020 under the project WR 19/58-2. ",
year = "2020",
month = oct,
doi = "10.1007/s00466-020-01891-5",
language = "English",
volume = "66",
pages = "963--977",
journal = "Computational Mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "4",
}