Analysis of an a posteriori error estimator for a variational inequality governed by the Stokes equations

In this work, a residual type a posteriori error estimator is presented for finite element approximations of a variational inequality arising in hydrodynamics, which is governed by the stationary Stokes equations with a nonlinear slip boundary condition of friction type. Reliability of the estimator is rigorously proved, and efficient error control is analyzed, both are based on an equality problem with a Lagrangian multiplier. And an algorithm of recovering the multiplier is also provided. Numerical results are reported to illustrate the good performance of the estimator in the adaptive solution of the variational inequality, as well as the availability of the multiplier.