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The nonconforming virtual element method (NCVEM) for the approximation of theweak solution to a general linear second-order non-selfadjoint indefiniteelliptic PDE in a polygonal domain is analyzed under reduced ellipticregularity. The main tool in the a priori error analysis is the connectionbetween the nonconforming virtual element space and the Sobolev space$H^1_0(\Omega)$ by a right-inverse $J$ of the interpolation operator $I_h$. Thestability of the discrete solution allows for the proof of existence of aunique discrete solution, of a discrete inf-sup estimate and, consequently, foroptimal error estimates in the $H^1$ and $L^2$ norms. The explicitresidual-based a posteriori error estimate for the NCVEM is reliable andefficient up to the stabilization and oscillation terms. Numerical experimentson different types of polygonal meshes illustrate the robustness of an errorestimator and support the improved convergence rate of an adaptivemesh-refinement in comparison to the uniform mesh-refinement.

A priori and a posteriori error analysis of the lowest-order NCVEM for second-order linear indefinite elliptic problems