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Beschreibung:
This contribution studies the influence of the pressure on the velocity error in finite element discretisations of the Navier–Stokes equations. Four simple benchmark problems that are all close to real-world applications convey that the pressure can be comparably large and is not to be underestimated. In fact, the velocity error can be arbitrarily large in such situations. Only pressure-robust mixed finite element methods, whose velocity error is pressure-independent, can avoid this influence. Indeed, the presented examples show that the pressure-dependent component in velocity error estimates for classical mixed finite element methods is sharp. In consequence, classical mixed finite element methods are not able to simulate some classes of real-world flows, even in cases where dominant convection and turbulence do not play a role.