(untitled) (Journal of Computational Mathematics, 1985)
For a large class of piecewise polynomial subspaces S^h defined on the regular mesh, W^1,∞-interior estimate \|u_h\|_1,∞,Ω_0 ≤ c\|u_h\|_-s,Ω_1, u_hS^hΩ_1 satisfying the interior Ritz equation is proved. For the finite element approximation u_h (of degree r-1) to u, we have W^1,∞-interior error estimate \|u-u_h\|_1,∞,Ω_0)≤ch^r-1 (\|u\|_r,∞,Ω_1+\|u\|_1,Ω). If the triangulation is strongly regular in Ω_1 and r=2 we obtain W^1,∞-interior superconvergence.