A Note on Pressure Approximation of First and Higher Order Projection Schemes for the Nonstationary Incompressible Navier-Stokes Equations (Journal of Computational Mathematics, 2018)
Projection methods are efficient operator-splitting schemes to approximate solutions ofthe incompressible Navier-Stokes equations. As a major drawback, they introduce spuriouslayers, both in space and time. In this work, we survey convergence results for higher orderprojection methods, in the presence of only strong solutions of the limiting problem; inparticular, we highlight concomitant difficulties in the construction process of accuratehigher order schemes, such as limited regularities of the limiting solution, and a lack ofaccurate initial data for the pressure. Computational experiments are included to comparethe presented schemes, and illustrate the difficulties mentioned.