Consistent pressure formulation of the Stokes problem and approximation thereof

Abstract

A non-conforming approximation of a non standard formulation of the generalized Stokes problem is proposed using continuous finite elements. The stability, convergence, and scalability properties of the method are numerically tested. Four key features of the method are as follows: (i) It is observed to converge optimally with pairs of equal order; (ii) The resulting algebraic system is simple to precondition; (iii) The formulation is pressure-robust for equal pairs; (iv) The formulation is particularly well adapted for the approximation of the time-dependent incompressible Navier-Stokes equations.