Carlo Lovadina, David Mora, Iván Velásquez:
A virtual element method for the von Kármán equations
In this article we propose and analyze a Virtual Element Method (VEM) to approximate the isolated solutions of the von Kármán equations, which describes 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 $H^2$ 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.
This preprint gave rise to the following definitive publication(s):
Carlo LOVADINA, David MORA, Iván VELáSQUEZ: A virtual element method for the von Kármán equations. ESAIM: Mathematical Modelling and Numerical Analysis, vol. 55, 2, pp. 533-560, (2021).