The virtual element method for linear elastodynamics models. Convergence, stability and dissipation-dispersion analysis
Abstract
We design the conforming virtual element method for the numerical approximation of the two dimensional elastodynamics problem. We prove stability and convergence of the semi-discrete approximation and derive optimal error estimates under - and -refinement in both the energy and the norms. The performance of the proposed virtual element method is assessed on a set of different computational meshes, including non-convex cells up to order four in the -refinement setting. Exponential convergence is also experimentally observed under p-refinement. Finally, we present a dispersion-dissipation analysis for both the semi-discrete and fully-discrete schemes, showing that polygonal meshes behave as classical simplicial/quadrilateral grids in terms of dispersion-dissipation properties.
Cite
@article{arxiv.1912.07122,
title = {The virtual element method for linear elastodynamics models. Convergence, stability and dissipation-dispersion analysis},
author = {P. F. Antonietti and G. Manzini and I. Mazzieri and H. Mourad and M. Verani},
journal= {arXiv preprint arXiv:1912.07122},
year = {2020}
}