A posteriori error estimates for the stabilization of low-order mixed finite elements for the Stokes problem

This paper studies a posteriori error estimates for the stabilization of low-order mixed finite elements for the Stokes problem. An interesting property of stabilized P 1 / P 0 and P 1 / P 1 finite element methods is proposed and used to construct new reliable and efficient error estimators. Moreover, an average technique is applied to improve the error estimators. Numerical results verify the theoretical results and show the improvement of such an average technique.