Energy norm a posteriori error estimation for divergence-free discontinuous Galerkin approximations of the Navier-Stokes equations

摘要

We develop the energy norm a posteriori error analysis of exactly divergence-free discontinuous RT{sub}k/Q{sub}k Galerkin methods for the incompressible Navier-Stokes equations with small data. We derive upper and local lower bounds for the velocity-pressure error measured in terms of the natural energy norm of the discretization. Numerical examples illustrate the performance of the error estimator within an adaptive refinement strategy.