Mixed virtual element methods for elastodynamics with weak symmetry

摘要: 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 stress is relaxed by rotation displacement, system second order differential equation time reduced to first equations introducing velocity. The proposed uses H ( div ) -conforming space k ≥ 1 discontinuous piecewise-polynomial spaces degree velocity rotation. For discretization, we use Crank–Nicolson scheme. Both semidiscrete fully discrete error estimates are robust nearly incompressible materials. Numerical experiments confirm our theoretical predictions.