An a posteriori finite element error analysis for the stokes equations

Conforming and nonconforming error estimators are presented and analyzed for the mixed finite element approximation of the Stokes problem. The estimators are obtained by solving local Poisson-type problems that do not involve boundary conditions, compatibility and balancing conditions, incompressibility constraint, or flux jumps across inter-element boundaries. The estimators are bounded from above and below by constant multiples of the actual error in an energy-like norm and can be used in adaptive h,p, and hp computations.