A C1-C0 virtual element discretization for a sixth-order elliptic equation

In this paper we study a virtual element method for the sixth-order elliptic problem with clamped and simply supported boundary conditions type. Using arguments like Ciarlet-Raviart method we introduce an auxiliary unknown w :=Delta u and we propose a weak formulation on H-2 x H-1 Sobolev space. A C-1 x C-0 virtual element discretization is proposed to approximate the solutions of the weak formulation. We also provide the convergence and error estimates results. Finally, several numerical examples illustrating the performance of the virtual element method are reported.