A posteriori finite-element output bounds for the incompressible Navier-Stokes equations:: Application to a natural convection problem

We present a new Neumann subproblem a posteriori finite-element procedure for the efficient calculation of rigorous, constant-free, sharp lower and upper bounds for linear and nonlinear functional outputs of the incompressible Navier-Stokes equations. We first formulate the bound procedure; we derive and discuss a bound error expression; and we then demonstrate the capabilities of the method with numerical results obtained for natural convection problems. We also implement an optimal adaptive refinement strategy based on a local elemental decomposition of the bound gap. (C) 2001 Academic Press.