Output functional control for nonlinear equations driven by anisotropic mesh adaption. The Navier-Stokes equations.

18/2007

Output functional control for nonlinear equations driven by anisotropic mesh adaption. The Navier-Stokes equations.

Tuesday 30th October 2007

Micheletti, Stefano; Perotto, Simona

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.