Adaptive Local Postprocessing Finite Element Method for the Navier-Stokes Equations

An adaptive local postprocessing finite element method for the Navier-Stokes equations is presented in this paper. We firstly solve the problem on a relative coarse grid to get a rough approximation. Then, we correct the rough approximation by solving a series of approximate local residual equations defined on some local fine grids, which can be implemented in parallel. In addition, we also propose a reliable local a posteriori error estimator and construct an adaptive algorithm based on the corresponding a posterior error estimate. Finally, some numerical examples are presented to verify the algorithm.