Projection methods are efficient operator-splitting schemes toapproximatesolutions of the incompressible Navier-Stokes equations.As a major drawback, they introduce spurious layers, both in space and time.In this work, we survey convergence results forhigher order projection methods, in the presence ofonly strong solutions of the limiting problem; in particular, wehighlight concomitantdifficulties in the construction process of accurate higher orderschemes, suchas limitedregularities of the limiting solution, and a lack of accurate initialdata for thepressure.Computational experiments are includedto compare the presented schemes, and illustrate the difficulties mentioned.