A unified framework for a posteriori error estimation for the Stokes problem

In this paper, a unified framework for a posteriori error estimation for the Stokes problem is developed. It is based on [H10 (Ω)] d-conforming velocity reconstruction and H(div, Ω)-conforming, locally conservative flux (stress) reconstruction. It gives guaranteed, fully computable global upper bounds as well as local lower bounds on the energy error. In order to apply this framework to a given numerical method, two simple conditions need to be checked. We show how to do this for various conforming and conform-ing stabilized finite element methods, the discontinuous Galerkin method, the Crouzeix–Raviart nonconforming finite element method, the mixed finite element method, and a general class of finite volume methods. Numerical experiments illustrate the theoretical developments