A nonconforming finite element method for the Stokes equations using the Crouzeix-Raviart element for the velocity and the standard linear element for the pressure

TL;DR

This paper introduces a finite element method for Stokes equations using Crouzeix-Raviart elements for velocity and linear elements for pressure, satisfying the inf-sup condition, supported by numerical experiments.

Contribution

It demonstrates the stability of a new finite element pairing for Stokes equations combining Crouzeix-Raviart and linear elements.

Findings

Inf-sup condition is satisfied for the proposed element pair

Numerical experiments confirm theoretical stability

Method effectively approximates Stokes flow

Abstract

We present a finite element method for Stokes equations using the Crouzeix-Raviart element for the velocity and the continuous linear element for the pressure. We show that the inf-sup condition is satisfied for this pair. Two numerical experiments are presented to support the theoretical results.