A Posteriori Error Estimate for Stabilized Low-Order Mixed FEM for the Stokes Equations

Abstract

This paper is concerned with a stabilized approach to low-order mixed finite element methods for the Stokes equations. We will provide a posteriori error analysis for the method. We present two a posteriori error indicators which will be demonstrated to be globally upper and locally lower bounds for the error of the finite element discretization. Finally two numerical experiments will be carried out to show the efficiency on constructing adaptive meshes.