Pressure robust finite element discretizations of the nonlinear Stokes equations

TL;DR

This paper introduces pressure robust finite element methods for nonlinear Stokes equations, ensuring velocity accuracy is unaffected by pressure errors, thus improving upon previous suboptimal methods.

Contribution

The paper proposes a first-order nonconforming Crouzeix-Raviart discretization that achieves pressure robustness for nonlinear generalized Stokes equations.

Findings

Velocity errors are independent of pressure errors.

The method improves upon suboptimal convergence rates.

The discretization is applicable to equations with $(r,\, ext{ extepsilon})$-structure.

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.