  Recovered finite element methods (R-FEM) have been recently introduced for
meshes consisting of simplicial and/or box-type meshes. Here, utilising the
flexibility of R-FEM framework, we extend their definition on polygonal and
polyhedral meshes in two and three spatial dimensions, respectively. A key
attractive feature of this framework is its ability to produce conforming
discretizations, yet involving only as many degrees of freedom as discontinuous
Galerkin methods over general polygonal/polyhedral meshes with potentially many
faces per element. A priori error bounds are shown for general linear, possibly
degenerate, second order advection-diffusion-reaction boundary value problems.
A series of numerical experiments highlights the good practical performance of
the proposed numerical framework.
