Improved parallel finite element methods for the stationary Navier–Stokes problem

In this study, two improved parallel finite element algorithms based on two-grid strategies are developed to approximate the stationary Navier–Stokes equations. Algorithms are devised to improve the existing local and parallel finite element methods to arrive at \(L^2\) $L^2$ optimal velocity approximation by considering one further coarse grid correction. Rigorously numerical analysis is established, and numerical experiments are reported to support the theoretical findings.