|Abstract:|| The contribution of this paper is twofold: firstly, a general
approach to the goal-oriented a posteriori analysis of nonlinear
partial differential equations is laid down, generalizing the standard
DWR method to Petrov-Galerkin formulations. This accounts for:
different approximations of the primal and dual problems;
nonhomogeneous Dirichlet boundary conditions, even
different on passing from the primal to the dual problem;
the error due to data approximation; the effect of stabilization
(e.g. for advective-dominated problems).
Secondly, moving from this framework, and employing anisotropic interpolation
error estimates, a sound anisotropic mesh adaption
procedure is devised for the numerical approximation of the
Navier-Stokes equations by continuous piecewise linear finite elements.
The resulting adaptive procedure is thoroughly addressed and
validated on some relevant test cases.