A High-Order Stabilization-Free Virtual Element Method for 3D Linear Elasticity

  • Bouchez, Timothée (INSA Lyon, CNRS, LaMCoS)
  • Gravouil, Anthony (INSA Lyon, CNRS, LaMCoS)
  • Blal, Nawfal (INSA Lyon, CNRS, LaMCoS)
  • Giacoma, Anthony (ANSYS France)
  • Delor, Emmanuel (ANSYS France)
  • Beley, Jean-Daniel (ANSYS France)

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The presented work introduces a high-order stabilization-free Virtual Element Method for 3D linear elasticity. To that end, the problem is formulated using the well known Hu-Washizu variational framework. The discrete interpolations of the strain, stress and displacement fields are then carefully chosen to ensure both computability and stability of the stiffness matrix. Finally, the convergence of the formulation is analyzed numerically, extending results of the 2D sf-VEM literature.