Recovery Type A Posteriori Error Estimate Of Crouzeixraviart Finite Element Method For The Stokes Equations

In this paper,the adaptive finite element method for Stokes equations based on gradient recovery is studied.We use the Crouzeix-Raviart element and piecewise constant element to discrete velocity field and pressure field,respectively.A super-convergence cluster recovery method(SCR)is proposed for the CR element.The least square fitting of the velocity at the sampling points is used to form a linear function,whose gradient is defined as the gradient at recovered points.We also used the SCR to recovery the value of the pressure,that is,applying the least square fitting to the pressure on the element patch to fit a linear function and the recovered pressure is defined by the obtained linear polynomial at the recovered point.Finally,we apply SCR method to a posterior error estimation and design the adaptive finite element method based on SCR.We also compared(SCR)gradient recovery and the residual posteriori error estimation in the adaptive finite element method for Stokes equations.The numerical results show the effectiveness of the recovered based posterior error estimator and the corresponding adaptive algorithm.