Estimates of the Distance to Exact Solutions of the Stokes Problem with Slip and Leak Boundary Conditions

Abstract

We deduce a posteriori error estimates of functional type for the stationary Stokes problem with slip and leak boundary conditions. The derived error majorants do not contain mesh dependent constants and are valid for a wide class of energy admissible approximations that satisfy the Dirichlet boundary condition on a part of the boundary. Different forms of error majorants contain global constants associated with Poincaré type inequalities or the stability (LBB) condition for the Stokes problem or constants associated with subdomains (if a domain decomposition is applied). It is proved that the majorants are guaranteed and vanish if and only if the functions entering them coincide with the respective exact solutions.