On the application of the P1mod element to incompressible flow problems

Abstrakt

We consider the application of the nonconforming P1mod element to the approximation of the velocity in the incompressible Stokes and Navier-Stokes equations. We prove the uniform validity of an inf-sup condition if the pressure is approximated by piecewise constant functions.

Under additional assumptions, we also prove the inf-sup condition for discontinuous piecewise linear approximations of the pressure.