Unconditional Superconvergence Error Estimates of Semi-Implicit Low-Order Conforming Mixed Finite Element Method for Time-Dependent Navier–Stokes Equations

Abstract

In this paper, the unconditional superconvergence error analysis of the semi-implicit Euler scheme with low-order conforming mixed finite element discretization is investigated for time-dependent Navier–Stokes equations. In terms of the high-accuracy error estimates of the low-order finite element pair on the rectangular mesh and the unconditional boundedness of the numerical solution in L∞-norm, the superclose error estimates for velocity in H1-norm and pressure in L2-norm are derived firstly by dealing with the trilinear term carefully and skillfully. Then, the global superconvergence results are obtained with the aid of the interpolation post-processing technique. Finally, some numerical experiments are carried out to support the theoretical findings.

Keywords

• Navier–Stokes equations
• linearized Euler scheme
• low-order conforming MFEM
• superconvergence error estimates