The virtual element method for linear elastodynamics models. Design, analysis, and implementation

Code:
58/2019
Title:
The virtual element method for linear elastodynamics models. Design, analysis, and implementation
Date:
Monday 30th December 2019
Author(s):
Antonietti, P.F; Manzini, G.; Mourad, H.M.; Verani, M.
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Abstract:
We design the conforming virtual element method for the numerical simulation of two dimensional time-dependent elastodynamics problems. We investigate the performance of the method both theoretically and numerically. We prove the stability and the convergence of the semi-discrete approximation in the energy norm and derive optimal error estimates. We also show the convergence in the $L^2$ norm. The performance of the virtual element method is assessed on a set of different computational meshes, including non-convex cells up to order four in the $h$-refinement setting. Exponential convergence is also experimentally seen in the $p$-refinement setting.