A Virtual Element Method on polyhedra with curved faces

In this paper we construct conforming Virtual Element approximations on domains with curved boundary and/or internal curved interfaces, both in two and three dimensions. Our approach allows to impose both Dirichlet and Neumann non-homogeneous boundary conditions, and provides, for degree of accuracy k ≥ 1, optimal convergence rates. Whenever the exact solution is a polynomial of degree k, local spaces of degree k ensure satisfaction of the patch test. The proposed method is theoretically analyzed in the two-dimensional case, whereas it is numerically validated both in two and three dimensions.