| Issue |
ESAIM: M2AN
Volume 55, Number 2, March-April 2021
|
|
|---|---|---|
| Page(s) | 533 - 560 | |
| DOI | https://doi.org/10.1051/m2an/2020085 | |
| Published online | 15 March 2021 | |
A virtual element method for the von Kármán equations
1
Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133 Milano, Italy
2
GIMNAP, Departamento de Matemática, Universidad del Bío-Bío, Concepción, Chile
3
CI 2MA, Universidad de Concepción, Concepción, Chile
4
Departamento de Ciencias Básicas, Universidad del Sinú-Elías Bechara Zainúm, Montería, Colombia
* Corresponding author: dmora@ubiobio.cl
Received:
6
September
2019
Accepted:
14
December
2020
In this article we propose and analyze a Virtual Element Method (VEM) to approximate the isolated solutions of the von Kármán equations, which describe the deformation of very thin elastic plates. We consider a variational formulation in terms of two variables: the transverse displacement of the plate and the Airy stress function. The VEM scheme is conforming in H2 for both variables and has the advantages of supporting general polygonal meshes and is simple in terms of coding aspects. We prove that the discrete problem is well posed for h small enough and optimal error estimates are obtained. Finally, numerical experiments are reported illustrating the behavior of the virtual scheme on different families of meshes.
Mathematics Subject Classification: 65N30 / 65N12 / 74K20 / 74S05 / 65N15
Key words: Virtual element method / von Kármán equations / error estimates / polygonal meshes
© EDP Sciences, SMAI 2021
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