We design the conforming virtual element method for the numerical approx- imation of the two-dimensional elastodynamics problem. We prove stability and convergence of the semidiscrete approximation and derive optimal error estimates under h- and p-refinement in both the energy and the L2 norms. The performance of the proposed virtual element method is assessed on a set of different computational meshes, including nonconvex cells up to order four in the h-refinement setting. Exponential convergence is also experimentally observed under p-refinement. Finally, we present a dispersion-dissipation analysis for both the semidiscrete and fully discrete schemes, showing that polygonal meshes behave as classical simplicial/quadrilateral grids in terms of dispersion-dissipation properties.

The arbitrary‐order virtual element method for linear elastodynamics models. Convergence, stability and dispersion‐dissipation analysis

P. F. Antonietti;I. Mazzieri;M. Verani
2021

Abstract

We design the conforming virtual element method for the numerical approx- imation of the two-dimensional elastodynamics problem. We prove stability and convergence of the semidiscrete approximation and derive optimal error estimates under h- and p-refinement in both the energy and the L2 norms. The performance of the proposed virtual element method is assessed on a set of different computational meshes, including nonconvex cells up to order four in the h-refinement setting. Exponential convergence is also experimentally observed under p-refinement. Finally, we present a dispersion-dissipation analysis for both the semidiscrete and fully discrete schemes, showing that polygonal meshes behave as classical simplicial/quadrilateral grids in terms of dispersion-dissipation properties.
elastodynamics, high-order methods, polygonal meshes, virtual element method
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1156302
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