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In this paper we analyze a lowest order virtual element method for the loadclassic reaction-convection-diffusion problem and the convection-diffusionspectral problem, where the assumptions on the polygonal meshes allow toconsider small edges for the polygons. Under well defined seminorms dependingon a suitable stabilization for this geometrical approach, we derive the wellposedness of the numerical scheme and error estimates for the load problem,whereas for the spectral problem we derive convergence and error estimates forthe eigenvalues and eigenfunctions. We report numerical tests to assess theperformance of the small edges on our numerical method for both problems underconsideration.

VEM discretization allowing small edges for the reaction-convection-diffusion equation: source and spectral problems