Towards fully computable error bounds for the incompressible Navier-Stokes equations

We obtain fully computable constant free a posteriori error bounds on simplicial meshes for: a nonconforming finite element approximations for a Stokes problem and a low-order conform- ing and low-order stabilized conforming finite element approximations for Poisson, Stokes and Advection-Reaction-Diffusion problems. All the estimators are completely free of unknown con- stants and provide guaranteed numerical bounds on natural norms, in terms of a lower bound for the inf-sup constant of the underlying continuous problem in the Stokes case. These estimators are also shown to provide a lower bound for the natural norms of the error up to a constant and higher order data oscillation terms. In the Stokes problem, the adaptive selection of the stabilization parameter appears as an application. Numerical results are presented illustrating the theory and the performance of the error estimators.EThOS - Electronic Theses Online ServiceGBUnited Kingdo