Finite element analysis of a pseudostress–pressure–velocity formulation of the stationary Navier–Stokes equations

Abstract

This article is concerned with a dual-mixed formulation of the Navier–Stokes equations which is based on the introduction of the pseudostress as a new unknown. The problem is approximated by a mixed finite element method in two and three dimensions: Raviart–Thomas elements of index $k\ge 0$ for the pseudostress tensor, and piecewise discontinuous polynomials of degree $k\ge 0$ for the velocity and the pressure. An existence result for the finite-element solution and convergence results are proved near a nonsingular solution. Finally, quasi-optimal error estimates, which improve those existing in the literature, are provided.