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In this paper we analyse the convergence properties of two-level, W-cycle andV-cycle agglomeration-based geometric multigrid schemes for the numericalsolution of the linear system of equations stemming from the lowest order$C^0$-conforming Virtual Element discretization of two-dimensional second-orderelliptic partial differential equations. The sequence of agglomeratedtessellations are nested, but the corresponding multilevel virtual discretespaces are generally non-nested thus resulting into non-nested multigridalgorithms. We prove the uniform convergence of the two-level method withrespect to the mesh size and the uniform convergence of the W-cycle and theV-cycle multigrid algorithms with respect to the mesh size and the number oflevels. Numerical experiments confirm the theoretical findings.

Agglomeration-based geometric multigrid schemes for the Virtual Element Method