A novel high-order implementation for the Navier–Stokes equations in the vorticity–velocity formulation is presented. It is based on the kinematic Laplacian equation (KLE) method introduced in a previous work as a low-order finite-element approach. Different aspects of the high-order implementation by spectral elements of this novel procedure are discussed. The well-known problem of a semi-infinite region of stationary fluid bounded by an infinite horizontal flat plate impulsively started is used in different ways to conduct comparative evaluation tests. This time dependent boundary-layer-development problem has an exact analytic solution, and may be regarded as a canonical problem for the subject of generation of vorticity boundary conditions in vorticity–velocity approaches. Results are analyzed and conclusions presented.Fil: Ponta, Fernando Luis. Michigan Technological University; Estados UnidosFil: Otero, Alejandro Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina