Pointwise error estimates for finite element solutions of the Stokes problem

摘要

In this paper pointwise error estimates for general finite element approximations of the Stokes problem are established on quasi-uniform grids in RN. The results obtained in this paper improve and extend the existing error estimates in the maximum norm for the Stokes problem. The new pointwise error estimates exhibit a more local dependence of the errors on the true solution and as a by-product provide logarithm-free bounds for all errors except the error of the velocity approximation of the lowest order.