New interpolation results and applications to finite element methods for elliptic boundary value problems

We consider the the interpolation problem between and , where Ω is a polygonal domain in and is the subspace of functions in H 1 (Ω) which vanish on the Dirichlet part ( ∂ Ω) D of the boundary of Ω. The main result is that the interpolation spaces and coincide. An application of this result to a nonconforming finite element problem is presented.