Analysis and computation of a pressure-robust method for the rotation form of the incompressible Navier–Stokes equations with high-order finite elements

Abstract

In this work, we develop a high-order pressure-robust method for the rotation form of the incompressible Navier–Stokes equations. The original idea is to change the velocity test functions in the discretization of trilinear and right hand side terms by using an H(div)-conforming velocity reconstruction operator. In order to match the rotation form and ease error analysis, a skew-symmetric discrete trilinear form containing the reconstruction operator is proposed, in which not only the velocity test function is changed. The corresponding well-posed discrete weak formulation stems straight from the classical inf-sup stable mixed conforming high-order finite elements, and it is proved to achieve the pressure-independent velocity errors. Optimal convergence rates of H1, L2-error for the velocity and L2-error for the Bernoulli pressure are completely established. Adequate numerical experiments are presented to demonstrate the theoretical results and remarkable performance of the proposed method.