Adaptive error control for finite element approximations of the lift and drag coefficients in viscous flow

Abstract. We derive estimates for the error in a variational approximation of the lift and drag coecients of a body immersed into a viscous ow governed by the Navier-Stokes equations. The variational approximation is based on computing a certain weighted average of a nite element approximation to the solution of the Navier-Stokes equations. Our main result is an a posteriori estimate that puts a bound on the error in the lift and drag coecients in terms of the local mesh size, a local residual quantity, and a local weight describing the local stability properties of an associated linear dual problem. The weight may be approximated by solving the dual problem numerically. The error bound is thus computable and can be used for quantitative error estimation; we apply it to design an adaptive nite element algorithm specically for the approximation of the lift and drag coecients. 1