A Petrov–Galerkin formulation for the incompressible Navier–Stokes equations using equal order interpolation for velocity and pressure

A new Petrov‐Galerkin method for the incompressible Navier‐Stokes equations is presented. The use of the so‐called ‘optimal upwind’ parameter in multidimensions is justified by a time‐scale analysis of the relevant physical processes. The resulting procedure circumvents the Babuška‐Brezzi condition and allows equal order interpolation for velocity and pressure to be used.