Abstract

We derive and analyze an a posteriori error estimate for the mini-element discretization of the Stokes equations. The estimate is based on the solution of a local Stokes problem in each element of the finite element mesh, using spaces of quadratic bump functions for both velocity and pressure errors. This results in solving a $9 \times 9$ system which reduces to two $3 \times 3$ systems easily invertible. Comparisons with other estimates based on a Petrov-Galerkin solution are used in our analysis, which shows that it provides a reasonable approximation of the actual discretization error. Numerical experiments clearly show the efficiency of such an estimate in the solution of self adaptive mesh refinement procedures.