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We present in a unified framework new conforming and nonconforming VirtualElement Methods (VEM) for general second order elliptic problems in two andthree dimensions. The differential operator is split into its symmetric andnon-symmetric parts and conditions for stability and accuracy on their discretecounterparts are established. These conditions are shown to lead to optimal$H^1$- and $L^2$-error estimates, confirmed by numerical experiments on a setof polygonal meshes. The accuracy of the numerical approximation provided bythe two methods is shown to be comparable.

Conforming and nonconforming virtual element methods for elliptic problems