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 Babuska-Brezzi condition and allows equal order interpolation for velocity and pressure to be used.

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