Quasi-optimal and pressure robust discretizations
of the Stokes equations

Pietro Zanotti (Università di Pavia).

Abstract.
We introduce some new discretizations of the stationary
Stokes equations based on general, possibly nonconforming,
inf-sup stable pairs of finite element spaces on simplicial
meshes. The discretizations are carefully designed in order
to achieve the following error estimates. The velocity
H^1-error is proportional to the corresponding best error
within the discrete velocity space and the sum of the
velocity H^1-error and of the pressure L^2-error is
proportional to the sum of the respective best errors.
The first estimate, in particular, was previously obtained
only by discretizations with the so-called conforming
and divergence-free pairs.