Unconditional stability and error estimates of the modified characteristics FEMs for the Micropolar Navier–Stokes Equations.

In this paper, the unconditional stability and optimal error estimate of the velocity, pressure and angular velocity for the modified characteristics FEMs of the unsteady Micropolar Naiver–Stokes Equations (MNSE) are presented. In this method, the nonlinear equation is linearized by the characteristic finite element method for dealing with the time derivative term and the convection term. Basing on the characteristic time-discrete system, the error function is split into a temporal error and a spatial error. With a rigorous analysis to the characteristic time-discrete system, we prove that the error between the numerical solution and the solution of the time-discrete system is τ -independent, where τ denotes the time stepsize. The stability results and optimal error estimates in L 2 norm and H 1 norm will be given. Finally, some numerical results will be provided to confirm our theoretical analysis. • The unconditional stability and optimal error estimate for the modified characteristics FEMs are presented. • The nonlinear equation is linearized by the characteristic method. • Basing on the characteristic time-discrete system, the error function is split into a temporal error and a spatial error. • The stability results and optimal error estimates in $L̂2$ norm and $Ĥ1$ norm will be given. [ABSTRACT FROM AUTHOR]