AGGLOMERATION-BASED GEOMETRIC MULTIGRID SCHEMES FOR THE VIRTUAL ELEMENT METHOD

In this paper we analyze the convergence properties of two-level, W-cycle, and V-cycle agglomeration-based geometric multigrid schemes for the numerical solution of the linear system of equations stemming from the lowest order C0-conforming virtual element discretization of two-dimensional second-order elliptic partial differential equations. The agglomerated tessellations in the sequence are nested, but the corresponding multilevel virtual discrete spaces are generally non-nested, thus resulting in non-nested multigrid algorithms. We prove the uniform convergence of the two-level method with respect to the mesh size and the uniform convergence of the W-cycle and the V-cycle multigrid algorithms with respect to the mesh size and the number of levels. Numerical experiments confirm the theoretical findings.