A sharp upper bound on the approximation order of smooth bivariate pp functions

Abstract

It is shown that the approximation order from bivariate piecewise polynomials of degree ≤k in Cρ is no better than k when k < 3ρ + 2 (even if only the three-direction mesh is considered). This complements the earlier result that the approximation order is full, i.e., equals k + 1, for any triangulation as soon as k ≥ 3ρ + 2. © 1993 Academic Press, Inc.