Mixed virtual element methods for elastodynamics with weak symmetry

We propose and analyze a mixed virtual element method for linear elastodynamics in velocity–stress formulation with weak symmetry. In this formulation, the symmetry of the stress is relaxed by the rotation of the displacement, and the system of second order differential equation in time is reduced t...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2019-06, Vol.353, p.49-71
Main Authors: Zhang, Baiju, Yang, Yan, Feng, Minfu
Format: Article
Language:English
Subjects:
Elastodynamics
Virtual elements
Weak symmetry
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Summary:We propose and analyze a mixed virtual element method for linear elastodynamics in velocity–stress formulation with weak symmetry. In this formulation, the symmetry of the stress is relaxed by the rotation of the displacement, and the system of second order differential equation in time is reduced to first order differential equations in time by introducing velocity. The proposed method uses H(div)-conforming virtual element space of order k(k≥1) for the stress and discontinuous piecewise-polynomial spaces of degree k for the velocity and rotation. For time discretization, we use the Crank–Nicolson scheme. Both semidiscrete and fully discrete error estimates are robust for nearly incompressible materials. Numerical experiments confirm our theoretical predictions. •A new mixed VEM for linear elastodynamics is proposed and analyzed.•This method leads to the treatment of general elements including non-convex elements.•Error estimates are shown to be uniform with respect to incompressibility parameter.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2018.12.020