Characteristic stabilized finite element method for the transient Navier–Stokes equations

Based on the lowest equal-order conforming finite element subspace (Xh, Mh) (i.e. P1–P1 or Q1–Q1 elements), a characteristic stabilized finite element method for transient Navier–Stokes problem is proposed. The proposed method has a number of attractive computational properties: parameter-free, avoiding higher-order derivatives or edge-based data structures, and averting the difficulties caused by trilinear terms. Existence,uniqueness and error estimates of the approximate solution are proved by applying the technique of characteristic finite element method. Finally, a serious of numerical experiments are given to show that this method is highly efficient for transient Navier–Stokes problem.