A Priori and A Posteriori Error Estimations for the Dual Mixed Finite Element Method of the Navier-Stokes Problem

This article is concerned with a dual mixedd formulation of the Navier-Stokes system in a polygonal domain of the plane with Dirichlet boundary conditions and its numerical approximation. The gradient tensor, a quantity of practical interest, is introduced as a new unknown. The problem is then approximated by a mixed finite element method. Quasi-optimal a priori error estimates are obtained. These a priori error estimates, an abstract nonlinear theory (similar to (Verfurth, RAIRO Model Math Anal Numer 32 (1998), 817-842)) and a posteriori estimates for the Stokes system from (Farhloul et al., Numer Funct Anal Optim 27 (2006), 831-846) lead to an a posteriori error estimate for the Navier-Stokes system. (C) 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 25: 843-869, 2009