Mixed virtual element methods for elastodynamics with weak symmetry

Abstract

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.