The arbitrary‐order virtual element method for linear elastodynamics models: convergence, stability and dispersion‐dissipation analysis. (21st December 2020)

• Record Type: Journal Article
• Authors: Antonietti, Paola F.; Manzini, Gianmarco; Mazzieri, Ilario; Mourad, Hashem M.; Verani, Marco
• Is Part Of: International journal for numerical methods in engineering. Volume 122:Number 4(2021)
• Page Start: 934
• Page End: 971
• Publication Date: 2020-12-21
• Subjects: elastodynamics -- high‐order methods -- polygonal meshes -- virtual element method; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6569
• Languages: English
• ISSNs: 0029-5981

Abstract

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.