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Discretization of Navier-Stokes' equations using pressure-robust finiteelement methods is considered for the high Reynolds number regime. To counteroscillations due to dominating convection we add a stabilization based on abulk term in the form of a residual-based least squares stabilization of thevorticity equation supplemented by a penalty term on (certain components of)the gradient jump over the elements faces. Since the stabilization is based onthe vorticity equation, it is independent of the pressure gradients, whichmakes it pressure-robust. Thus, we prove pressure-independent error estimatesin the linearized case, known as Oseen's problem. In fact, we prove an$O(h^{k+\frac12})$ error estimate in the $L^2$-norm that is known to be thebest that can be expected for this type of problem. Numerical examples areprovided that, in addition to confirming the theoretical results, show that thepresent method compares favorably to the classical residual-based SUPGstabilization.

A pressure-robust discretization of Oseen's equation using stabilization in the vorticity equation