On the -saturation property for functions from

This short note is devoted to the proof of the L q -saturation property for functions from the Sobolev space W 2 , p ( Ω ) , p > d / 2 , on sequences of conformal, possibly anisotropic, simplicial meshes for spaces of arbitrary dimension d . The proof completes the theory of optimal meshes minimizing the L q -error ( 0 < q ≤ p ) of P 1 -interpolation and the theory of quasi-optimal meshes which are achievable approximations of the optimal meshes (Agouzal et al., 2009, 2010 [2,3], Agouzal et al., 2010 [4]).