A priori and a posteriori error estimations for the dual mixed finite element method of the Navier‐Stokes problem

Abstract

AbstractThis article is concerned with a dual mixed 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 (Verfürth, 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. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009