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In this study, we propose a virtual element scheme to solve the Darcy problemin three physical dimensions. The main novelty, here proposed, is that curvedelements are naturally handled without any degradation of the solutionaccuracy. In fact, in presence of curved boundaries, or internal interfaces,the geometrical error introduced by planar approximations may dominate theconvergence rate limiting the benefit of high-order approximations. We considerthe Darcy problem in its mixed form to directly obtain, with our numericalscheme, accurate and mass conservative fluxes without any post-processing. Animportant step to derive this new scheme is the actual computation ofpolynomials over curved polyhedrons, here presented and discussed. Finally, weshow the theoretical analysis of the scheme as well as several numericalexamples to support our findings

Bend 3d Mixed Virtual Element Method for Elliptic Problems