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

Antonietti, Paola F.; Manzini, Gianmarco; Mazzieri, Ilario; Mourad, Hashem M.; Verani, Marco

doi:10.1002/nme.6569

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

Journal Article · Mon Dec 21 00:00:00 EST 2020 · International Journal for Numerical Methods in Engineering

DOI:https://doi.org/10.1002/nme.6569· OSTI ID:1804784

Antonietti, Paola F. ^[1]; ^[2]; Mazzieri, Ilario ^[1]; Mourad, Hashem M. ^[3]; Verani, Marco ^[1]

MOX, Dipartimento di Matematica Politecnico di Milano Milano Italy
Group T‐5, Theoretical Division Los Alamos National Laboratory Los Alamos New Mexico USA
Group T‐3, Theoretical Division Los Alamos National Laboratory Los Alamos New Mexico USA

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 semidiscrete approximation and derive optimal error estimates under h ‐ and p ‐refinement in both the energy and the L ² 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.

View Accepted Manuscript (Publisher)

Sponsoring Organization:: USDOE

OSTI ID:: 1804784

Journal Information:: International Journal for Numerical Methods in Engineering, Journal Name: International Journal for Numerical Methods in Engineering Journal Issue: 4 Vol. 122; ISSN 0029-5981

Publisher:: Wiley Blackwell (John Wiley & Sons)Copyright Statement

Country of Publication:: United Kingdom

Language:: English

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