Approximating partial derivatives of first and second order by quadratic spline quasi-interpolants on uniform meshes

Given a bivariate function f defined in a rectangular domain Ω, we approximate it by a C1 quadratic spline quasi-interpolant (QI) and we take partial derivatives of this QI as approximations to those of f. We give error estimates and asymptotic expansions for these approximations. We also propose a simple algorithm for the determination of stationary points, illustrated by a numerical example.