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

In this work, we introduce in the context of linear elasticity, and for the first time in the literature up to the authors knowledge, a high-order stabilization-free Virtual Element Method. To that end, the continuous problem is formulated using a Hu-Washizu variational approach. The strain and stress fields are then discretized using polynomial interpolations, while an enhanced virtual element space involving a serendipity projection operator is used for the discrete displacement. The strain and stress polynomial order is selected to ensure stability of the formulation, while the serendipity projection operator reduces the overall number of degrees of freedom. The convergence behavior of the proposed method is finally numerically analyzed on various mesh types.