Pressure robust finite element discretizations of the nonlinear Stokes equations

Abstract

We present first-order nonconforming Crouzeix-Raviart discretizations for the nonlinear generalized Stokes equations with $(r,\epsilon )$-structure. Thereby the velocity-errors are independent of the pressure-error; i.e., the method is pressure robust. This improves suboptimal rates previously experienced for non pressure robust methods.